HP_Prime_MATH: Manual

Manual HP_Prime_MATH Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M i HP_Prime_MATH: Manual Open Library ID: OL60452436M Copyright © 2025 Dietmar Gerald Schrausser, Creative Commons Attribution 4.0 International. Edition 1. Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M ii Contents Introduction 1 Functions Correlation 1 Exposure functions 7 Functions of integration 9 Distribution functions 11 Probability 20 Combinatorics 23 Resampling 24 Complex plane 27 Source codes CAS functions 31 User functions 60 Application functions 69 Graph 3D 72 Solve 73 Data Functions 75 Lists 76 Matrices 77 References 99 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 1 HP_Prime_MATH: Manual Dietmar G. Schrausser Karl-Franzens University, Graz, Austria Introduction Mathematical and statistical applications for HP Prime (s. HP Inc., 2017; Schrausser, 2025a, b). Algorithms are presented in context with the corresponding scope of application (s. Functions). CAS programs (i), HP Prime User functions (ii) and functions for HP Prime Applications (iii) are listed in alphabetical order (s. Source Codes), for a comparison to corresponding SCHRAUSSER-MAT functions (Schrausser, 2022a) see Table 2. In addition to the source codes of the functions, raw data sets are provided for correlationas well as resampling-methods (s. Data). On mathematical statistical methods in general see e.g. Cox and Hinkley (1974), Bortz and Weber (2005), Lehmann and Romano (2008) or Bortz and Schuster (2010), Schrausser (2024a) provides a comprehensive overview of the most important distribution functions and corresponding algorithms. Introducing works on resampling methods are given by e.g. Good (2006) or Beasley and Rodgers (2009), for calculus and theory of functions see e.g. Meyberg and Vachenauer (2001a, b) or Remmert and Schumacher (2002), on complex numbers in the complex plane see e.g. Burckel (2021) and Vince (2021). For the history of statistical inference in general see e.g. Stigler (1986) and Hald (1990, 1998, 2003, 2007), historical foundations of mathematics are thematized and discussed in e.g. Suter (1887), Heath (1921a, b), Boyer (1968), Neugebauer (1969), Ewald (1996a, b), Katz (2009) or Merzbach and Boyer (2011). Functions Correlation To measure the degree of a linear relation between variables, Karl Pearson (1904) was developing statistical procedures for biometry including the correlation and regression coefficients based on the works of Bravais (1844) and Galton (1877) who introduced the symbol 𝑟, on the then designation of the term reversion. Table 1. Appropriate correlation coefficients; product-moment or Pearson correlation 𝑟𝑥𝑦, Spearman’s rank correlation coefficient rho 𝜌, biserial (or biseral) coefficients 𝑟𝑏𝑖𝑠, 𝑟𝑝𝑏, 𝑟𝑏𝑖𝑠𝑅 and phi coefficient 𝛷 at the corresponding scale levels, interval i, ordinal o, and nominal n. i o n i 𝑟𝑥𝑦 o 𝜌 ¹ n 𝑟𝑏𝑖𝑠, 𝑟𝑝𝑏 𝑟𝑏𝑖𝑠𝑅 𝛷 ² ¹) also Kendall’s tau 𝜏 (1938) or Somers’ 𝐷 (1962). ²) also tetrachoric correlation 𝑟𝑡𝑒𝑡. Creative Commons Attribution 4.0 International Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 2 The methodological apparatus of factor analysis as a further and broader concept, based on multiple regression and matrix calculation was first discussed by Charles Edward Spearman (1904), later the initial developed took place by Louis Leon Thurstone (1931, 1934, 1935; s. also Cattell, 1966). [KOR|IC_M] [rxy|RED|tr|TRW|pRW|pRWx] [E01] Pearson product-moment correlation coefficient 𝑟𝑥𝑦 Bravais (1844), Galton (1877), Pearson (1904, 1905). 𝑟𝑥𝑦=𝜎𝑥𝑦 2 𝜎𝑥⋅𝜎𝑦, 𝜎𝑥𝑦 2=∑ (𝑥𝑖−𝑥)⋅(𝑦𝑖−𝑦) 𝑛𝑖=1 𝑛 with 𝑡(𝑑𝑓)=𝑟⋅√𝑛−2 √1−𝑟2 where 𝑟2 = coefficient of determination, redundancy 𝑑𝑒𝑡%=𝑟2⋅100 𝜎𝑥𝑦 2 = covariance of 𝑥 and 𝑦 𝑑𝑓 = 𝑛−2 [RHO] Spearman’s 𝜌 Equivalent to the product moment correlation when rank values are present (s. Spearman, 1904). 𝑟𝑠=𝜌=1−6⋅∑𝑑𝑖2𝑛𝑖=1 𝑛⋅(𝑛2−2) with 𝑡(𝑑𝑓)=𝜌⋅√𝑛−2 √1−𝜌2;𝑛≥30 where 𝑑𝑖 = rank difference of 𝑥𝑖 and 𝑦𝑖 𝑑𝑓 = 𝑛−2 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 3 [TAU] Kendall’s tau 𝜏𝑎 Without adjustment for ties (s. Kendall, 1938). 𝜏𝑎=1− 2⋅𝑛𝑑 0.5⋅𝑛⋅(𝑛−1), with 𝑧=3⋅𝜏𝑎⋅√𝑛⋅(𝑛−1) √2⋅(2⋅𝑛+5);𝑛>10 alternatively 𝑧= 𝑛𝑐−𝑛𝑑 √1 18⋅𝑛⋅(𝑛−1)⋅(2⋅𝑛+5) where 𝑛 = total number of pairs 𝑛𝑑 = number of discordant pairs 𝑛𝑐 = number of concordant pairs, with 𝑛𝑐=(𝑛2)−𝑛𝑑 [DELTA2] Somers’ 𝐷 For binary data [0,1] (s. Somers, 1962). 𝐷𝑌𝑋=𝑛1,1 𝑛−𝑛1,0 𝑛 where 𝑛 = total number of pairs 𝑛1,1 = number of pairs with 𝑌=1,𝑋=1 𝑛1,0 = number of pairs with 𝑌=1,𝑋=0 [rpbis] Point biserial correlation coefficient 𝑟𝑝𝑏 Also point biseral. 𝑟𝑝𝑏=𝑥1−𝑥0 𝜎𝑥⋅√𝑛1⋅𝑛2 𝑛2 with 𝑡(𝑑𝑓)=𝑟𝑝𝑏⋅√𝑛−2 √1−𝑟𝑝𝑏 2 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 4 where 𝑑𝑓 = 𝑛−2 [rbis|srbis|zrbis|prbis] Biserial correlation coefficient 𝑟𝑏𝑖𝑠 Pearson (1909), see e.g. Tate (1955), also called biseral. 𝑟𝑏𝑖𝑠=𝑥1−𝑥0 𝜎𝑥⋅𝑛1⋅𝑛2 𝜗⋅𝑛2 with 𝑧=𝑟𝑏𝑖𝑠 𝜎𝑟𝑏𝑖𝑠, 𝜎𝑟𝑏𝑖𝑠=√𝑛1⋅𝑛2 𝜗⋅𝑛⋅√𝑛 where 𝜗= 1 √2⋅π⋅𝑒−𝐹(𝑝=𝑛0 𝑛)2 2 [rbisR|U_1|U_2|zrbisR|prbisR] Rank biserial correlation coefficient 𝑟𝑏𝑖𝑠𝑅 Also rank biseral correlation, corresponds to the effect size for the Mann–Whitney 𝑈 test (Mann & Whitney, 1947). 𝑟𝑏𝑖𝑠𝑅=2𝑛⋅(𝑖1−𝑖2) with 𝑧= 𝑈−𝑛1⋅𝑛2 2 √𝑛1⋅𝑛2⋅(𝑛+1) 12 where 𝑈=𝑛1⋅𝑛2+𝑛12+𝑛1 2−∑𝑥𝑖 𝑛1 𝑖=1 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 5 [PHC] [PHI|xPHI|pPHI] Phi coefficient 𝛷 Yule (1912). 𝛷= 𝑎⋅𝑑−𝑏⋅𝑐 √(𝑎+𝑐)⋅(𝑏+𝑑)⋅(𝑎+𝑏)⋅(𝑐+𝑑) with 𝜒(𝑑𝑓) 2=𝑛⋅𝛷2 where 𝑑𝑓=1 [PHC] [rtet|srtet|prtet] Tetrachoric correlation 𝑟𝑡𝑒𝑡 Pearson (1900a), Everitt (1910, 1912), s. e.g. Brown (1977), Digby (1983), also Bonett and Price (2005) or Long et al. (2009), proposed approximate algorithm. 𝑟𝑡𝑒𝑡=cosπ 1+√𝑏⋅𝑐 𝑎⋅𝑑 with 𝑧=𝑟𝑡𝑒𝑡 𝜎𝑟𝑡𝑒𝑡, 𝜎𝑟𝑡𝑒𝑡=√𝑎+𝑏 𝑛⋅𝑎+𝑐 𝑛⋅𝑐+𝑑 𝑛⋅𝑏+𝑑 𝑛 𝑛⋅1 𝜗𝑥⋅𝜗𝑦 where 𝜗𝑥=1 √2⋅π⋅e−𝐹(𝑝=𝑐+𝑑 𝑛)2 2 𝜗𝑦=1 √2⋅π⋅e−𝐹(𝑝=𝑏+𝑑 𝑛)2 2 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 6 [PKR] [rxy_z|zrxy_z|prxy_z|ry_xz] Partial correlation 𝑟𝑥𝑦⋅𝑧 𝑟𝑥𝑦⋅𝑧=𝑟𝑥𝑦−𝑟𝑥𝑧⋅𝑟𝑦𝑧 √1−𝑟𝑥𝑧 2⋅√1−𝑟𝑦𝑧 2 with 𝑧=𝑍𝑟𝑥𝑦⋅𝑧⋅√𝑛−2 and semi partial correlation 𝑟𝑦(𝑥⋅𝑧)=𝑟𝑥𝑦−𝑟𝑥𝑧⋅𝑟𝑦𝑧 √1−𝑟𝑥𝑧 2, [ZCor] [Zr|rZ] Fisher 𝑍-transformation Fisher (1915). 𝑍=12⋅ln1+𝑟 1−𝑟 with 𝑧= 𝑍 √1 𝑛−3 and 𝑟𝑍=𝑒2⋅𝑍−1 𝑒2⋅𝑍+1 [Zrr|prr] Fisher 𝑍 difference, Cohen’s 𝑞 Cohen (1988, p. 110). 𝜃=𝑑𝑍=𝑍𝑟1−𝑍𝑟2 with 𝑧= 𝑑𝑍 √1 𝑛1−3+1 𝑛2−3 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 13 [Q01_|AMG|HM_] Harmonic mean 𝑥 𝑥=𝐻= 𝑛 ∑𝑥𝑖−1𝑛𝑖=1 , 𝑥󰇘=∑𝑛𝑖 𝑘𝑖=1 ∑𝑛𝑖 𝑥𝑖 𝑘𝑖=1 [Q01_] Coefficient of variation 𝜔 𝜔=𝜎𝑥;𝑥>0 [MDN] Mean dispersion 𝑑 Schrausser (2022a, p. 33). 𝑑=∑ |𝑥𝑖−𝑥| 𝑛𝑖=1 ∑1 𝑛𝑖=1 ;𝑥𝑖≠𝑥, 𝛿=𝜎⋅𝜁⋅√𝑛 𝑛−1=𝜎⋅𝜁 with 𝜎𝑑=𝜎⋅ 1 2⋅𝜁⋅√𝑛 where 𝜁𝑑=𝛿=45 [NVTLG] [E01|F02|F03] Standard normal distribution 𝑓(𝑥=𝑧) De Moivre (1738), Gauss (1809, 1823). 𝑓(𝑧)=𝜗= 1 √2⋅𝜋⋅e−𝑧2 2 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 14 with 𝐹(𝑧)=𝑝=∫ 𝑓(𝑧)𝑑𝑧 𝑧 −∞ , 𝑓′(𝑧)=∂𝑓(𝑧) ∂𝑧 [NVXY] [F01Z] Bivariate normal distribution 𝑓(𝑧1,𝑧2) 𝑓(𝑧1,𝑧2)=𝜗= 1 2⋅π⋅√1−𝑟2⋅e −1 2⋅(1−𝑟2)⋅(𝑧12−2⋅𝑟⋅𝑧1⋅𝑧2+𝑧22), 𝐹(𝑧1,𝑧2)=1=∬ 𝑓 ∞ −∞ (𝑧1,𝑧2)𝑑𝑧1𝑑𝑧2 where 𝑟 = correlation 𝑟(𝑧1,𝑧2) [tVTLG|F06_] [F02|F06|F03Z] Student’s 𝑡-distribution 𝑓(𝑥=𝑡) Lüroth (1876), Pearson (1895), Gosset (1908). 𝑓(𝑡)=𝜗=𝛤𝑑𝑓+1 2 𝛤𝑑𝑓 2⋅(𝑑𝑓⋅π)−12⋅(1+𝑡2 𝑑𝑓)−𝑑𝑓+1 2 with 𝐹(𝑡,𝑑𝑓)=𝑝=∫ 𝑓(𝑡)𝑑𝑡 𝑡 −∞ where 𝛤𝑥=∫ 𝑦𝑥−1⋅e−𝑦𝑑𝑦+𝑐 ∞ 0 [ch2VTLG|F07_] [F02|F07|F03Z] 𝜒2-distribution 𝑓(𝑥=𝜒2) Helmert (1876), Pearson (1900b, 1914), Elderton (1902), Plackett (1983). 𝑓(𝜒2)=𝜗= 1 2𝑑𝑓 2⋅𝛤𝑑𝑓 2⋅𝜒2𝑑𝑓 2−1⋅e−𝜒2 2 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 15 with 𝐹(𝜒2,𝑑𝑓)=1−𝑝𝛼2=∫ 𝑓(𝜒2)𝑑𝜒2 𝜒2 0 where 𝛤𝑥=∫ 𝑦𝑥−1⋅e−𝑦𝑑𝑦+𝑐 ∞ 0 [FVTLG] [F02|F03Z] 𝐹 distribution 𝑓(𝑥=𝐹) Fisher (1924), Snedecor (1934), Scheffé (1959). 𝑓(𝐹)=𝜗=𝛤𝑑𝑓1+𝑑𝑓2 2 𝛤𝑑𝑓1 2⋅𝛤𝑑𝑓2 2⋅(𝑑𝑓1 𝑑𝑓2)𝑑𝑓1 2⋅𝐹𝑑𝑓1 2−1⋅(1+𝑑𝑓1 𝑑𝑓2⋅𝐹)−𝑑𝑓1+𝑑𝑓2 2 with 𝐹(𝐹,𝑑𝑓1,𝑑𝑓2)=1−𝑝𝛼2=∫𝑓(𝐹)𝑑𝐹 𝐹 0 where 𝛤𝑥=∫ 𝑦𝑥−1⋅e−𝑦𝑑𝑦+𝑐 ∞ 0 [Q02_] Third standardized moment, skewness 𝛼3 𝛼3=∑𝑧𝑖3𝑛𝑖=1 𝑛, 𝛼3=𝑛⋅∑ (𝑥𝑖−𝑥)3 𝑛𝑖=1 (𝑛−1)⋅(𝑛−2)⋅𝜎3 with 𝑧=𝛼3 √6𝑛 [Q02_] Fourth standardized moment, excess kurtosis 𝛼4 𝛼4=∑𝑧𝑖4𝑛𝑖=1 𝑛−3, Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 16 𝛼4=𝑛⋅(𝑛+1)⋅∑ (𝑥𝑖−𝑥)4 𝑛𝑖=1 −3⋅∑ (𝑥𝑖−𝑥)2 𝑛𝑖=1 ⋅∑ (𝑥𝑖−𝑥)2⋅(𝑛−1) 𝑛𝑖=1 (𝑛−1)⋅(𝑛−2)⋅(𝑛−3)⋅𝜎4 with 𝑧= 𝛼4 2⋅√6𝑛 [SMG] [CIx] Estimated standard error of mean 𝜎𝑥, confidence interval 𝐶𝐼𝑝 Neyman (1937) introduced the confidence interval into statistical hypothesis testing vs. Fisher’s null hypothesis testing, the Neyman–Pearson lemma (Neyman & Pearson, 1933; Lehmann, 1993). 𝜎𝑥=√𝜎⋅ 𝑛 𝑛−1 𝑛 with 𝐶𝐼𝑝=𝑥±𝑡(1−1−𝑝 2,𝑛−1)⋅𝜎𝑥, 𝐶𝐼𝑝=𝜃±𝑡(1−1−𝑝 2,𝑑𝑓)⋅𝜎𝜃 where 𝑝 = probability 𝑛 = number of cases [CIXY] [CIr] [E01] Standard error of prediction 𝜎𝑦𝑥 , confidence interval 𝐶𝐼𝑝 𝜎𝑦𝑥=𝜎𝑦⋅√1−𝑟2 with 𝐶𝐼𝑝=𝑦𝑥±𝑧(1−1−𝑝 2)⋅𝜎𝑦𝑥 where 𝑝 = probability 𝑟 = correlation 𝑦 = predicted value 𝑦 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 17 [EPSILON] [EFG|EFR] [E01] Effect size 𝜖, Cohen’s 𝑑 Cohen (1977, 1988, p. 20, p. 49, 1992), Borenstein et al. (1997), Borenstein et al. (2001). 𝜖=𝑑=𝜇1−𝜇0 𝜎 , 𝑑𝑣=𝑑 √1−𝑟 with 𝑥𝑐𝑟𝑖𝑡 𝛽=𝜇1±𝑡(𝑝𝑐𝑟𝑖𝑡,𝑑𝑓)⋅𝜎𝑥, 𝑡(𝑑𝑓) 𝛼=𝑥01−𝜇0 𝜎𝑥, 𝑡(𝑑𝑓) 𝛽=𝑥01−𝜇1 𝜎𝑥 where 𝑑𝑣 = 𝑑 for paired samples 𝑟 = correlation Power = 𝑝1−𝛽=1−𝑝𝛽 [EPSILON2] Optimal effect size 𝜖𝑝 𝜖𝑝=√(2⋅𝑡(𝑝𝑐𝑟𝑖𝑡,𝑑𝑓))2 𝑛, [EPSILON2] Optimal alpha level 𝑡(𝑜𝑝𝑡,𝑑𝑓) 𝛼=√𝜖2⋅𝑛 2 [TKV] [tTKV|pTKV] Variance difference 𝑡-test For paired samples (𝑥1|𝑥2). 𝜃=𝑑𝜎2=𝜎12−𝜎22 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 18 with 𝑡(𝑑𝑓)=𝑑𝜎2⋅√𝑛−2 2⋅√𝜎12⋅𝜎22⋅(1−𝑟2) where 𝑑𝑓 = 𝑛−2 [TV_] [tTV|pTV] Paired 2-sample 𝑡-test 𝜃=𝑥𝑑=∑𝑥(𝑖,1)−𝑥(𝑖,2) 𝑛𝑖=1 𝑛 with 𝑡(𝑑𝑓)=𝑥𝑑 𝜎𝑥𝑑, 𝜎𝑥𝑑=√∑(𝑥(𝑖,1)−𝑥(𝑖,2))2 𝑛𝑖=1 −(∑𝑥(𝑖,1)−𝑥(𝑖,2) 𝑛𝑖=1 )2 𝑛 𝑛−1 ⋅1 √𝑛 where 𝑥𝑑 = mean of the differences of 𝑥1 and 𝑥2 values 𝑑𝑓 = 𝑛−1 [TU_] [tTU_|pTU_|tTUx|pTUx] Unpaired 2-sample 𝑡-test 𝜃=𝑑𝑥=𝑥1−𝑥2 with 𝑡(𝑑𝑓)=𝑑𝑥 𝜎𝑑𝑥, 𝜎𝑑𝑥=√∑(𝑥(𝑖,1)−𝑥1)2 𝑛1 𝑖=1 +∑(𝑥(𝑖,2)−𝑥2)2 𝑛2 𝑖=1 𝑛−2 ⋅√1 𝑛1+1 𝑛2 where 𝑑𝑥 = difference of the means 𝑥1 and 𝑥2 𝑑𝑓 = 𝑛−2 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 19 [TT_] [tTT_|pTT_] One-sample 𝑡-test 𝜃=𝑑𝑥𝑦=𝑥−𝑦 with 𝑡(𝑑𝑓)=𝑑𝑥𝑦 √𝜎2 𝑛−1 where 𝑑𝑥𝑦 = difference between sample mean 𝑥 and test value 𝑦 𝑑𝑓 = 𝑛−1 [ABT1] [x2F|p2F|zBN|pzBN] 𝜒2-test for independence 𝜒2=∑(𝑓𝑒𝑖−𝑓𝑏𝑖)2 𝑓𝑏𝑖 𝑛 𝑖=1 with 𝑧=𝑏−𝑏+𝑐 2 √𝑏+𝑐 4 [VFCH] [x4F|p4F|x4FY|p4FY|z4F|pz4F] 2 × 2 𝜒2-test for independence For Yates’s correction for continuity see Yates (1934). 𝜒2=𝑁⋅(𝑎⋅𝑑−𝑏⋅𝑐)2 (𝑎+𝑏)⋅(𝑐+𝑑)⋅(𝑎+𝑐)⋅(𝑏+𝑑), 𝜒𝑌𝑎𝑡𝑒𝑠 2=𝑁⋅(|𝑎⋅𝑑−𝑏⋅𝑐|⋅𝑁2)2 (𝑎+𝑏)⋅(𝑐+𝑑)⋅(𝑎+𝑐)⋅(𝑏+𝑑);4<𝑓𝑒<7 with 𝑧= 𝑑−𝑁⋅𝑃𝑑 √𝑁⋅𝑃𝑑⋅(1−𝑃𝑑)−𝑁⋅(𝑁−1)⋅𝑃𝑑⋅(𝑃𝑑−𝑃𝑑) Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 20 where 𝑓𝑒 = expected frequency 𝑃𝑑=(𝑑+𝑏)⋅(𝑐+𝑑) 𝑁2 𝑃𝑑=(𝑑+𝑏−1)⋅(𝑐+𝑑−1) (𝑁−1)2 𝑑𝑓=1 [VFCH] [xMN|pMN|xMNY|pMNY] McNemar’s 𝜒2-test for paired 2 × 2 contingency tables with dichotomous trait McNemar (1947). 𝜒2=(𝑏−𝑐)2 𝑏+𝑐 , 𝜒2=(|𝑏−𝑐|−12)2 𝑏+𝑐 ;20<(𝑏+𝑐)<30 Probability Since until the Renaissance a probable opinion was merely confirmed by an authority and hence there was no further concept of inductive evidence (see Hacking, 1975; Hald, 2003, p. 31), an objective representation of probability as such was first discussed by Antoine Arnauld and Pierre Nicole (1662, 1682, 1693; c.f. also Arnauld et al., 1970; van Evra, 1997; Dessì & Albury, 1997 or Finocchiaro, 1997). The binomial distribution is primarily attributable to de Moivre (1711, 1718, 1738) and Jacob Bernoulli (1713), see also Schneider (2005a, b). Although not included as function, due to its considerability in this context, the configuration frequency analysis, CFA should be mentioned particularly (c.f. Krauth, 1973; Krauth & Lienert, 1993). An account of the systematics and logic of dependent probabilities within the framework of Bayes’ theorem (Bayes & Price, 1763; c.f. Stigler, 2018) can be found in Schrausser (2024c). The arguably most important methods regarding the calculation of probability parameters are implemented. [Ch|ChA|ChB] Arcsine transformation, Cohen’s ℎ Cohen (1988, p. 181). 𝜃=𝑝1−𝑝2, ℎ=2⋅sin−1√𝑝1−2⋅sin−1√𝑝2 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 21 with 𝑝1=sin(2⋅sin−1√𝑝2+ℎ 2)2, 𝑝2=−sin(−2⋅sin−1√𝑝1+ℎ 2)2 where probabilities = 𝑝1, 𝑝2 [ABT1] [ADDP] [E01] Additive probability for independent events 𝑢𝑝(∪𝑛𝐴) Corresponds to the geometric distribution 𝑓(𝑋≤𝑟|𝑝). 𝑢𝑝(∪𝑛𝐴)=1−(1−𝑝𝐴)𝑛 where 𝑛 = number of events 𝐴 𝑝𝐴 = probability of event 𝐴 [GMVTLG] Geometric distribution 𝑓(𝑋≤𝑟|𝑝) Corresponds to the additive probability 𝑢𝑝(∪𝑛𝐴). 𝑓(𝑋=𝑟|𝑝)=𝑃𝑛=𝑝⋅𝑞𝑟 with 𝑓(𝑋≤𝑟|𝑝)=𝑝𝑛=∑𝑝⋅𝑞𝑖 𝑟 𝑖=0 where 𝑝 = probability of event 𝑟+1=𝑛 = number of events [NBNMVTLG] [NBINOM] [E01] Negative binomial distribution 𝑓(𝑋≤𝑟|𝑟,𝑝) With 𝑘=1 it corresponds to the geometric distribution 𝑓(𝑋≤𝑟|𝑝) and the additive probability 𝑢𝑝(∪𝑛𝐴). 𝑓(𝑋=𝑟|𝑟,𝑝)=𝑃𝑛=(𝑘+𝑟−1)! 𝑟!⋅(𝑘−1)!⋅𝑝𝑘⋅𝑞𝑟 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 22 with 𝑓(𝑋≤𝑟|𝑟,𝑝)=𝑝𝑛=∑(𝑘+𝑖−1)! 𝑖!⋅(𝑘−1)!⋅𝑝𝑘⋅𝑞𝑖 𝑟 𝑖=0 where 𝑟+𝑘=𝑛 = number of events 𝑘 = number of successes [ABT1] [BINOM|zBN|pzBN] [E01] Exact binomial test 𝑓(𝑋=𝑏|𝑏,𝑐)=𝑃0=(𝑏+𝑐)! 𝑏!⋅𝑐! ⋅2−𝑏⋅2−𝑐 with 𝑓(𝑋≤𝑏|𝑏,𝑐)=𝑝=𝑝𝑒𝑥𝑎𝑐𝑡1=∑ (𝑏+𝑐)! 𝑖!⋅(𝑏+𝑐−𝑖)! 𝑏 𝑖=0 ⋅2−𝑖⋅2−(𝑏+𝑐−𝑖);𝑝≤12, 𝑝𝑒𝑥𝑎𝑐𝑡1=(1−𝑝)+𝑃0;𝑝>12 also 𝑧=𝑏−𝑏+𝑐 2 √𝑏+𝑐 4 [FX_] [z4F|pz4F] Exact hypergeometric 2 × 2 test Fisher Exact test (Fisher, 1922; Agresti, 1992). 𝑓(𝑋=𝑎|𝑎,𝑏,𝑐,𝑑)=𝑃0=(𝑎+𝑏)!⋅(𝑐+𝑑)!⋅(𝑎+𝑐)!⋅(𝑏+𝑑)! 𝑁!⋅𝑎!⋅𝑏!⋅𝑐!⋅𝑑! with 𝑓(𝑋≤𝑎|𝑎,𝑏,𝑐,𝑑)=𝑝𝑒𝑥𝑎𝑐𝑡1=∑𝑃 𝑎 𝑖=1 𝑖;𝑝≤12, 𝑓(𝑋≥𝑎|𝑎,𝑏,𝑐,𝑑)=𝑝𝑒𝑥𝑎𝑐𝑡1=∑𝑃 𝑛 𝑖=𝑎 𝑖;𝑝>12 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 29 zrbis ZBS Rank biserial prbisR KBR rbisR ZBR U_1 U_2 zrbisR Phi PHC PHI KPH pPHI KPM xPHI XKP Tetrachoric PHC prtet KTET rtet STET srtet ZTET Partial PKR prxy_z PKR rxy_z ZKR ry_xz zrxy_z Fisher Z ZCor rZ FZR Zr RFZ SFZ Z difference, Cohen's q prr ZRR Zrr Averaged Fisher Z mZ mr GFZ mZ Multiple, Cohen's f² MCORR2 Cf2 MKR FMCORR SKM MCORR BMK pMCORR MBC SCR FMK Exposure Value Ev AEv E03 Ev E02 TEv Aperture Av for time Tv AvTv Aperture Av for speed S AvS E03 Aperture Av shift from time Tv AvTvk Aperture Av shift from speed S AvSk Integration Circular pi F01 F05 Spherical pi F01Z Gamma F01Z GAMMA F04 Distribution Standardizing Q01_ zVAL Z__ zVALp Z_P ZWERT Z_W Quantity proportion npz Weighted arithmetic mean AMG AMG Geometric mean AMG GM_ GM_ Q01_ Harmonic mean AMG HM_ HM_ Q01_ Coefficient of variation Q01_ SDV Mean dispersion MDN D__ Standard normal distribution NVTLG F02 DZW F03 PZD Bivariate normal distribution NVXY F01Z Student's t F06_ F02 DTW tVTLG F03Z PTD F06 Chi² ch2VTLG F02 DXW F07_ F03Z PXD F07 F FVTLG F02 DFW Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 30 F03Z PFD Third standardized moment Q02_ SCH SHP SSH ZSH Fourth standardized moment Q02_ EXZ EZP SEX ZEX Estimated standard error of mean SMG CIx SMG SMX Standard error of prediction CIXY CIr E01 Effect size, Cohen's d EPSILON EFG E01 EFG EFR Optimal effect size EPSILON2 EFS Optimal alpha level EPSILON2 OPP Variance difference TKV pTKV TKV tTKV Paired 2-sample t-test TV_ pTV TV_ tTV Unpaired 2-sample t-test TU_ pTU_ TU_ pTUx TUX tTU_ tTUx One-sample t-test TT_ pTT_ TT_ tTT_ Chi²-test for independence ABT1 p2F EDX pzBN ZBN x2F zBN 2 × 2 chi²-test for independence VFCH p4F VFX p4FY VFYX pz4F ZFX x4F x4FY z4F McNemar's chi²-test VFCH pMN MNX pMNY MNYX xMN xMNY Probability Arcsine transformation, Cohen's h ch chA chB Additive probability for independent events ABT1 ADDP E01 AWN Geometric GMVTLG GMP GMW Negative binomial NBNMVTLG NBINOM E01 NBP NBW Exact binomial test ABT1 BINOM E01 BN0 pzBN BN1 zBN BN2 Exact hypergeometric 2 × 2 test FX_ pz4F FX0 z4F FX1 FX2 Combinatorics Permutation matrix PRM2 P_M PM_ Permutation matrix to class m PRM3 nk ; P2M PMM PMW Variation matrix PRM4 VRW VWM Variation matrix, dependent 2 sample design PRM5 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 31 Resampling Permutation test P for 2 paired samples PV_ Randomized permutation test mP for 2 paired samples mPV_ Permutation test P for 2 independent samples PU_ Randomized permutation test mP for 2 independent samples mPU_ Bootstrap test Bt for 2 independent samples BtU_ Complex plane Argand diagram CPLX F02Z CPLX2 Complex function CPLHX Source codes CAS functions To create or edit: To select, insert and execute: A ABT1.pas //ABT1()/D.G.SCHRAUSSER/2022 //Binomialp[A1:bA2:c]/Addp[C1:pC2:nC3:k] #cas ABT1():= BEGIN STARTAPP("Arbeitsblatt"); STARTVIEW(1) 5▸A1; 5▸A2; =A1+A2▸A3; 0.5▸B1; =BINOMIAL_CDF(A3,B1,A1)▸B4 0.5▸C1; 8▸C2; 1▸C5; =1-(1-C1)^C2▸D4; =Σ((C5+I-1)!/(I!*(C5-1)!)*C1^C5*(1-C1)^I,I,0,C2-C5)▸D6; END; #end // ABT2.pas //ABT2(cell count a,b,c,d)/D.G.SCHRAUSSER/2025 //2×2 chi-squared test for independence //Observed frequencies abcd fb //Expected frequencies fe //Probabilities p(A^B), p(B|A), p(A|B) //Chi-squared with 2-tailed p //e.g.ABT2(17,12,14,24)[Spreadsheet] #cas ABT2(a,b,c,d):= BEGIN STARTAPP("Arbeitsblatt"); STARTVIEW(1) Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 32 "A1"▸B1 "A2"▸C1 "A1"▸E1 "A2"▸F1 "B1"▸A2 "B2"▸A3 "B1"▸A5 "B2"▸A6 "B1"▸A8 "B2"▸A9 "B1"▸A11 "B2"▸A12 a▸B2 b▸C2 c▸B3 d▸C3 D2:==B2+C2 D3:==B3+C3 B4:==B2+B3 C4:==C2+C3 D4:==B2+C2+B3+C3 E5:==B2/D4 F5:==C2/D4 g5:==D2/D4 E6:==B3/D4 F6:==C3/D4 g6:==D3/D4 E7:==B4/D4 F7:==C4/D4 g7:==g5+g6 E2:==B2/D2 F2:==C2/D2 g2:==E2+F2 E3:==B3/D3 F3:==C3/D3 g3:==E3+F3 B5:==B2/B4 B6:==B3/B4 B7:==B5+B6 C5:==C2/C4 C6:==C3/C4 C7:==C5+C6 B8:==E7*D2 B9:==E7*D3 C8:==F7*D2 C9:==F7*D3 D13:==D4*(B2*C3-C2*B3)^2/((B2+C2)*(B3+C3)*(B2+B3)*(C2+C3)) B11:==(B2-B8)^2/B8 B12:==(B3-B9)^2/B9 C11:==(C2-C8)^2/C8 C12:==(C3-C9)^2/C9 D11:==((B2-B8)^2/B8)+(C2-C8)^2/C8 D12:==((B3-B9)^2/B9)+(C3-C9)^2/C9 B13:==B11+B12 C13:==C11+C12 g11:==1-(CHISQUARE_CDF(1,D11)) g12:==1-(CHISQUARE_CDF(1,D12)) g13:==1-(CHISQUARE_CDF(1,D13)) E11:==1-(CHISQUARE_CDF(1,B11)) E12:==1-(CHISQUARE_CDF(1,B12)) E13:==1-(CHISQUARE_CDF(1,B13)) F11:==1-(CHISQUARE_CDF(1,C11)) F12:==1-(CHISQUARE_CDF(1,C12)) F13:==1-(CHISQUARE_CDF(1,C13)) END; Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 33 #end // AMG.pas //AMG()/D.G.SCHRAUSSER/2025 //Weighted arithmetic, geometric and harmonic mean #cas AMG():= BEGIN //L1()(2) provided size(L1)▸L3(1) mean(L1)(1)▸L3(2) MAKELIST(L1(x)(1)*L1(x)(2),x,1,L3(1))▸L2 ΣLIST(L1)(2)▸L3(3) Σ(L2)/L3(3)▸L3(4) L3(3) NTHROOT (product((L1(x)(1))^L1(x)(2),x,1,L3(1)))▸L3(5) L3(3)/(Σ(L1(x)(2)/L1(x)(1),x,1,L3(1)))▸L3(6) //n,AM,sumni,GAM,GGM,GHM L3 END; #end // B BNMVTLG.pas //BNMVTLG(p[e],a=k,n)/D.G.SCHRAUSSER/2025 //e.g.BNMVTLG(0.5,5,10) #cas BNMVTLG(P,K,N):= BEGIN B=0; FOR I FROM 0 TO K DO BINOMIAL(N,P,I)▸L4(I) B=B+L4(I) END; D5=L4;L4={} FOR I FROM 0 TO N DO BINOMIAL(N,P,I)▸L5(I); END; D6=L5;L5={}; STARTAPP("Statistiken_1_Var"); STARTVIEW(1); "D5"▸H1(1);5▸H1(3); "D6"▸H2(1);5▸H2(3); //p RETURN(B); END; #end // BtU_.pas //BtU_(simulation cycles B)/D.G.SCHRAUSSER/2025 //Bootstrap method, Bt //2 independent samples (x|g) //e.g.BtU_(1000) #cas BtU_(B):= BEGIN //L1L2 provided {}▸L3;{}▸L4 {}▸L5;{}▸L6 0▸M11 0▸M12 0▸M2 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 34 SIZE(L1)▸N1 SIZE(L2)▸N2 N=N1+N2 ABS(mean(L1)-mean(L2))▸Q02 ΣLIST(L1)▸Q011 ΣLIST(L2)▸Q012 // CONCAT(L1,L2)▸L9 MSGBOX("BtU") FOR J FROM 1 TO B DO // FOR A FROM 1 TO N DO L9(RANDINT(N))▸L0(A) END; FOR A FROM 1 TO N1 DO L0(A)▸L3(A) END; FOR A FROM 1 TO N2 DO L0(N1+A)▸L4(A) END; ABS(mean(L3)-mean(L4))▸QJ2 ΣLIST(L3)▸QJ11 ΣLIST(L4)▸QJ12 IF QJ11≥Q011 THEN M11=M11+1 END; IF QJ12≥Q012 THEN M12=M12+1 END; IF QJ2≥Q02 THEN M2=M2+1 END; QJ11▸L5(J) QJ2▸L6(J) END; // SORT(L5)▸L5 SORT(L6)▸L6 {}▸L9 {}▸L0 N1,N2,[Q011,Q012,Q02],M11/B,M12/B,M2/B END; #end // C ch2VTLG.pas //ch2VTLG(chi-squared,df)/D.G.SCHRAUSSER/2025 //e.g.ch2VTLG(2.65,1)[AdvancedGraphing] #cas ch2VTLG(C2569,A7485):= BEGIN G=Gamma(A7485/2) //P=∫((1/(2^(A7485/2)*G))*X^((A7485/2)-1)*e^(-X/2),X,0,C) P=CHISQUARE_CDF(A7485,C2569) A7485▸A C2569▸C "Y=(1/(2^(A/2)*G))*X^((A/2)-1)*e^(-X/2)"▸V1 "Y<(1/(2^(A/2)*G))*X^((A/2)-1)*e^(-X/2) AND Y>0 AND X<C AND X>0"▸V2 STARTAPP("Erweiterte_Grafiken"); STARTVIEW(1); [1-P] END; #end // CIXY.pas //CIXY(x,y'CI)/D.G.SCHRAUSSER/2022 //Standard error of prediction sy'x, CI //e.g.CIXY(3,0.99[ZWERT,Statistics_2_Var,Spreadsheet,AdvancedGraphing] #cas CIXY(X,C):= BEGIN Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 35 //C1C2 provided STARTAPP("Statistiken_2_Var"); STARTVIEW(−6) A=Corr B=sY D=MeanY PredY(X)▸L3(2); √(1-A^2)*B*NORMALD_ICDF(1-((1-C)/2))▸L3(4) L3(4)+L3(2)▸L3(3) L3(2)-L3(4)▸L3(1) C▸L3(5) ZWERT(L3(1),D,B)▸L4(1) ZWERT(L3(2),D,B)▸L4(2) ZWERT(L3(3),D,B)▸L4(3) L4(1)▸U L4(3)▸O ZWERT(X,MeanX,sX)▸Q STARTAPP("Arbeitsblatt"); "ŷ-"▸A1;L3(1)▸B1;L4(1)▸C1 "ŷ"▸A2;L3(2)▸B2;L4(2)▸C2 "ŷ+"▸A3;L3(3)▸B3;L4(3)▸C3 "±"▸A4;L3(4)▸B4;L3(4)/B▸C4 "CI"▸A5;L3(5)▸B5; STARTAPP("Erweiterte_Grafiken"); STARTVIEW(1) "Y=A*X"▸V3 "Y>0 AND (Y<A^(-1)*X AND Y>A*X) OR Y<0 AND (Y>A^(-1)*X AND Y<A*X)"▸V4 "Y=√(1-X^2)"▸V5 "Y=-1*√(1-X^2)"▸V6 "X<A AND X>0 AND Y<A AND Y>0"▸V7 CAS((X,Y)->((Y<O) AND (Y>U)) AND ((X==Q))▸V0) //y'-,y',y'+,CI,sy'x,CIp RETURN(L3); END; #end // CPLHX.pas //CPLHX(complex number,a+bi)/D.G.SCHRAUSSER/2022 //e.g.CPLHX(2+i/2),[AdvancedGraphing] #cas CPLHX(C):= BEGIN C▸Z1 RE(Z1)▸R IM(Z1)▸I Z1▸L1(1) ABS(Z1)▸L1(2) ARG(Z1)▸L1(3) "Y=R*X"▸V1 "Y=I"▸V2 "Y=√((R*X)^2+I^2)"▸V3 "Y=(I/ABS(I))*(π/2)-ATAN((R/I)*X)"▸V4 STARTAPP("Erweiterte_Grafiken") STARTVIEW(1) RETURN(L1); END; #end // CPLX.pas //CPLX(complex number,a+bi)/D.G.SCHRAUSSER/2022 //e.g.CPLX(2+i/2),[AdvancedGraphing] #cas CPLX(C):= Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 36 BEGIN C▸Z1 RE(Z1)▸R IM(Z1)▸I ABS(Z1)▸L1(1) R▸X▸J I▸K "Y=√(1-X^2)"▸V5 "Y=-1*√(1-X^2)"▸V6 "Y=I"▸V7 "X=R"▸V8 "X<R AND X>0 AND Y>0 AND Y≤0.01"▸V0 "Y=(I/R)*X AND Y>0 AND X<R"▸V9 IF I<0 THEN "Y=(I/R)*X AND Y<0 AND X<R"▸V9 END; IF R<0 THEN "Y=(I/R)*X AND Y>0 AND X>R"▸V9 END; IF I<0 AND R<0 THEN "Y=(I/R)*X AND Y<0 AND X>R"▸V9 END; ARG(Z1)▸L1(2) CONVERT(L1(2)_rad,1_deg)▸L1(3) RETURN(L1); END; #end // CPLX.pas //CPLX2(complex number,a+bi)/D.G.SCHRAUSSER/2022 //e.g.CPLX2(2+i/2),[CPLX,Spreadsheet]// #cas CPLX2(C):= BEGIN CPLX(C) STARTAPP("Arbeitsblatt"); "z"▸A1;Z1▸B1 "|z|"▸A2;L1(1)▸B2 "∡π"▸A3;L1(2)▸B3 "∡°"▸A4;L1(3)▸B4 END; #end // D DELTA2.pas //DELTA2()/D.G.SCHRAUSSER/2025 //Somers' D for binary values [0,1] #cas DELTA2():= BEGIN SIZE(L1)▸N {}▸L3 0▸X01 0▸X02 FOR I FROM 1 TO N DO IF L1(I)=1 AND L2(I)=1 THEN X01=X01+1 END; IF L1(I)=1 AND L2(I)=0 THEN X02=X02+1 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 37 END; END; X01/N▸L3(1) X02/N▸L3(2) L3(1)-L3(2)▸L3(3) //pA,pB,D approx(L3) END; #end // E EPSILON.pas //EPSILON(x1,m1,m2,s12,d)/D.G.SCHRAUSSER/2022 //e.g.EPSILON(106,100,110,15,25) #cas EPSILON(X,M,N,S,D):= BEGIN G=Gamma((D+1)/2)/Gamma(D/2) E=(N-M)/S P=1-∫(G*(D*π)^(-1/2)*(1+(X^2/D))^(-(D+1)/2),X,−∞,E) T=(((N+M)/2)-M)/S H=1-∫(G*(D*π)^(-1/2)*(1+(X^2/D))^(-(D+1)/2),X,−∞,T) Q=(X-M)/S R=1-∫(G*(D*π)^(-1/2)*(1+(X^2/D))^(-(D+1)/2),X,−∞,Q) U=∫(G*(D*π)^(-1/2)*(1+(X^2/D))^(-(D+1)/2),X,−∞,(X-N)/S) B=1-U "X>T AND X≤T"▸V1 "X>Q AND X≤Q"▸V2 // D▸K "X>0 AND X<E AND Y<0 AND Y>-0.01"▸V3 "Y<(G*(K*π)^(-1/2)*(1+((E-X)^2/K))^(-(K+1)/2)) AND Y>0 AND X>Q"▸V6 "Y<(G*(K*π)^(-1/2)*(1+((E-X)^2/K))^(-(K+1)/2)) AND Y>0 AND X<Q"▸V7 "Y=(G*(K*π)^(-1/2)*(1+((E-X)^2/K))^(-(K+1)/2))"▸V8 "Y=(G*(K*π)^(-1/2)*(1+((X)^2/K))^(-(K+1)/2))"▸V0 "Y<(G*(K*π)^(-1/2)*(1+((X)^2/K))^(-(K+1)/2)) AND Y>0 AND X>Q"▸V9 E▸L2(1);P▸L3(1);N▸L1(1) T▸L2(2);H▸L3(2);T*S+M▸L1(2) Q▸L2(3);R▸L3(3);Q*S+M▸L1(3) U▸L4(3);B▸L5(3) STARTAPP("Arbeitsblatt"); "ε"▸A1;L2(3)▸B1;L2(2)▸C1;L2(1)▸D1; "x"▸A2;L1(3)▸B2;L1(2)▸C2;L1(1)▸D2; "α"▸A3;L3(3)▸B3;L3(2)▸C3;L3(1)▸D3; "β"▸A4;L4(3)▸B4; "1-β"▸A5;L5(3)▸B5; STARTAPP("Erweiterte_Grafiken") STARTVIEW(1) RETURN(L2(1),L3(3),L4(3)); END; #end // EPSILON2.pas //EPSILON2(epsilon,n,df,pcrit)/D.G.SCHRAUSSER/2022 //e.g.EPSILON2(0.38,100,99,0.95) //optimal effect size epsilon //optimal alpha t //1-p(alpha opt t) #cas EPSILON2(E,N,D,K):= BEGIN Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 38 #t opt niv V=√(E^2*N)/2▸L6(2) P=1-STUDENT_CDF(D,V)▸L6(3) #e opt eff stke L=√((2*STUDENT_ICDF(D,K))^2/N)▸L6(1) "X>0 AND X<L AND Y<0 AND Y>-0.02"▸V1 RETURN(L6); END; #end // EPSOLON3.pas //EPSILON3(100,110,15,25,0.99) #cas EPSILON3(M,N,S,D,K):= BEGIN F=STUDENT_ICDF(D,K) M+S*F▸L7(1) N-S*F▸L7(2) "X>E-F AND X≤E-F AND Y>0 AND Y<(G*(K*π)^(-1/2)*(1+((E-X)^2/K))^(-(K+1)/2))" ▸V4 "X>F AND X≤F AND Y>0 AND Y<(G*(K*π)^(-1/2)*(1+((X)^2/K))^(-(K+1)/2))"▸V5 RETURN(L7); END; #end // F FVTLG.pas //FVTLG(F,df1,df2)/D.G.SCHRAUSSER/2025 //e.g.FVTLG(2.8,10,5) #cas FVTLG(F,A,B):= BEGIN F▸X CAS(Gamma((A+B)/2))▸H CAS(Gamma(A/2))▸D CAS(Gamma(B/2))▸E CAS(H/(D*E))▸C CAS((X,Y)->Y=C*((A/B)^(A/2)*X^((A/2)-1)*(1+(A/B)*X)^(−(((A+B)/2)))) AND X>0 ▸V2) CAS((X,Y)->Y<C*((A/B)^(A/2)*X^((A/2)-1)*(1+(A/B)*X)^(−(((A+B)/2)))) AND Y>0 AND X<F AND X>0▸V1) FISHER_CDF(A,B,X)▸P STARTAPP("Erweiterte_Grafiken") STARTVIEW(1) P,[1-P] END; #end // FX.pas //FX_(cell count a,b,c,d)/D.G.SCHRAUSSER/2025 //e.g.FX_(1,2,3,1) //Exact hypergeometric 4-field test according to R. A. Fisher //(Fisher Exact Test): Hypergeometric probability p to cell a of the 4-field initial arrangement for all possible arrangements a //Exact significance levels p[exact1], p[exact2] #cas FX_(a,b,c,d):= BEGIN {}▸L1 1▸S Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 45 // N1,N2,[Q011,Q012,Q02],M11/M,M12/M,M2/M END; #end // mPU2.pas //mPU2(simulation cycles M)/D.G.SCHRAUSSER/2025 //Permutation test in the random sampling model, //randomized permutation, p-value not randomized, mP //2 independent samples (x|g) //e.g.mPU2(100) #cas mPU2(M):= BEGIN //L1L2 provided // {}▸L3;{}▸L4 {}▸L5;{}▸L6 0▸M11 0▸M12 0▸M02 0▸X 0▸J SIZE(L1)▸N1 SIZE(L2)▸N2 N=N1+N2 // MAKELIST(x+1,x,0,N-1)▸L7 MAKELIST(0,x,0,1)▸L51 MAKELIST(x+1,x,0,N1-1)▸L71 // ABS(mean(L1)-mean(L2))▸Q02 ΣLIST(L1)▸Q011 ΣLIST(L2)▸Q012 // MSGBOX("mPU") WHILE J<M DO // FOR A FROM 1 TO N DO {RANDOM(),L7(A)}▸L0(A) END; //diff {}▸L9 SORT(L0)▸L31 // FOR A FROM 1 TO N1 DO L31(A)▸L51;L51(2)▸L6(A) END; sort(L0)▸L9 FOR A FROM 1 TO N DO L9(A)▸L8;L8(2)▸L9(A) END; {}▸L8 L9==L7▸V // IF DIFFERENCE(L6,L71)≠{} AND V=0 THEN J+1▸J CONCAT(L1,L2)▸L8 FOR A FROM 1 TO N1 DO L8(L9(A))▸L3(A) END; FOR A FROM 1 TO N2 DO L8(L9(N1+A))▸L4(A) END; ABS(mean(L3)-mean(L4))▸QJ2 ΣLIST(L3)▸QJ11 ΣLIST(L4)▸QJ12 IF QJ11≥Q011 THEN M11=M11+1 END; Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 46 IF QJ12≥Q012 THEN M12=M12+1 END; IF QJ2≥Q02 THEN M02=M02+1 END; // QJ11▸L5(J) QJ2▸L6(J) // ELSE X+1▸X END; //IF diff END; //M // SORT(L5)▸L5 SORT(L6)▸L6 {}▸L8 {}▸L0 // X,J,N1,N2,[Q011,Q012,Q02],M11/M,M12/M,[M02/M] END; #end // mPV_.pas //mPV_(simulation cycles M)/D.G.SCHRAUSSER/2025 //Permutation test in the random sampling model, //randomized permutation, p-value not randomized, mP //2 paired samples (x1|x2) //e.g.mPV_(100) #cas mPV_(M):= BEGIN //L1()(2) provided 0▸M11;0▸M12;0▸M2 SIZE(L1)(1)▸N //sum,Q0 ΣLIST(L1)▸L2;ΣLIST(L2.^2)▸Q02 L2(1)▸Q011;L2(2)▸Q012 // MSGBOX("mPV") FOR A FROM 1 TO M DO //mP // FOR I FROM 1 TO N DO RANDINT(0,1)▸L8(I) END; FOR J FROM 1 TO N DO IF L8(J)=1 THEN REVERSE(L1(J))▸L3(J) ELSE L1(J)▸L3(J) END; END; //J ΣLIST(L3)▸L4;ΣLIST(L4.^2)▸Q2 L4(1)▸Q11;L4(2)▸Q12 Q11▸L5(A) Q12▸L6(A) Q2▸L7(A) IF Q11≥Q011 THEN M11=M11+1 END; IF Q12≥Q012 THEN M12=M12+1 END; IF Q2≥Q02 THEN M2=M2+1 END; // END;//mP // SORT(L5)▸L5;SORT(L6)▸L6;SORT(L7)▸L7 //n,Q011,Q012,Q02,p11,p12,p2 N,[Q011,Q012,Q02],M11/M,M12/M,M2/M END; #end // mZ.pas //mZ()/D.G.SCHRAUSSER/2025 //Averaged Fisher-Z, mean r/[ZCor] Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 47 #cas mZ():= BEGIN //L1(N)(2) provided size(L1)▸N FOR I FROM 1 TO N DO ZCor(L1(I,1),L1(I,2))(1)▸L3 L3(1)▸L2(I) END; Σ((L1(I,2)-3)*L2(I),I,1,N)/Σ(L1(I,2)-3,I,1,N)▸L3(1) L3(2):=(e^(2*L3(1))-1)/(e^(2*L3(1))+1) //n,_Z,_r N,L3 END; // N NBNMVTLG.pas //NBNMVTLG(k,p[e],n,m)/D.G.SCHRAUSSER/2025 //e.g.NBNMVTLG(1,0.2,8,10) #cas NBNMVTLG(K,P,N,M):= BEGIN B=0 FOR I FROM 0 TO N-K DO ((K+I-1)!/(I!*(K-1)!))*P^K*(1-P)^I▸L4(I+1) B=B+L4(I+1) END D7=L4;L4={} FOR I FROM 0 TO M-1 DO ((K+I-1)!/(I!*(K-1)!))*P^K*(1-P)^I▸L5(I+1) END D8=L5;L5={}; STARTAPP("Statistiken_1_Var"); STARTVIEW(1); "D7"▸H3(1);5▸H3(3); "D8"▸H4(1);5▸H4(3); //p RETURN(B); END; #end // NVTLG.pas //NVTLG(z[crit],tail[1/2])/D.G.SCHRAUSSER/2025 //e.g.NVTLG(1.96,2) #cas NVTLG(Z,S):= BEGIN "Y=(1/√(2*π))*e^((-1/2)*(X)^2)"▸V9 "Y<(1/√(2*π))*e^((-1/2)*(X)^2) AND Y>0 AND X<C"▸V8 NORMALD_CDF(Z)▸P; IF S=2 THEN "Y<(1/√(2*π))*e^((-1/2)*(X)^2) AND Y>0 AND X<C AND X>−C"▸V8 P=P-(1-P); END; C=Z; STARTAPP("Erweiterte_Grafiken"); STARTVIEW(1); //p-value RETURN(P); END; #end // Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 48 P pCor.pas //pCor(correlation r,n)/D.G.SCHRAUSSER/2025 //e.g.pCor(0.94,4) #cas pCor(r,n):= BEGIN t=(r*√(n-2))/√(1-r^2) p=STUDENT_CDF(n-2,t) 2*p▸p2 IF p>0.5 THEN 2*(1-p)▸p2 END; //t-value, p-value, p2 [t],p,[p2] END; #end // PHC.pas //PHC(cell count a,b,c,d)/D.G.SCHRAUSSER/2025 //e.g.PHC(17,12,14,24) //Phiand tetrachoric correlation #cas PHC(a,b,c,d):= BEGIN a+b+c+d▸N a+b▸z1;c+d▸z2 a+c▸s1;b+d▸s2 z1/z2▸Z01;s1/s2▸S01 IF z2<z1 THEN Z01=1/Z01 END; IF s2<s1 THEN S01=1/S01 END; VFX=(N*(a*d-b*c)^2)/((a+b)*(c+d)*(a+c)*(b+d)) VFC=1-CHISQUARE_CDF(1,VFX) KPH=(a*d-b*c)/sqrt(((a+b)*(c+d)*(a+c)*(b+d))) KPM=sqrt(Z01*S01) KTET=cos(π/(1.+√(b*c/(a*d)))) STET=sqrt((((((a+b)/N))*(((a+c)/N))*(((c+d)/N))*(((b+d)/N))/N))) STET=STET*(1/(((1/(sqrt(2*π)))*e^(-normald_icdf(((c+d)/N))^2/2))*((1/(sqrt(2 *π)))*e^(-normald_icdf(((b+d)/N))^2/2)))) ZTET=KTET/STET P=normald_cdf(ZTET) IF P>0.5 THEN P=1-P END; P*2▸P2 //n,TET,z,p1,p2,phi,phimax,chi2,p2 N,[KTET],[ZTET],P,[P2],[KPH,KPM],[VFX],[VFC] END; #end // PKR.pas //PKR()/D.G.SCHRAUSSER/2025 //Partial corr rxy.z[pCor,ZCor] #cas PKR():= BEGIN //L1L2L3 provided size(L1)▸N df=N-2 //rxy FOR I FROM 1 TO N DO L1(I)▸L5(1) L2(I)▸L5(2) L5▸L4(I) Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 49 END; approx(correlation(L4))▸r0 pCor(r0,N)(3)▸pr0 //rxz FOR I FROM 1 TO N DO L1(I)▸L5(1) L3(I)▸L5(2) L5▸L4(I) END; approx(correlation(L4))▸r1 pCor(r1,N)(3)▸pr1 //ryz FOR I FROM 1 TO N DO L2(I)▸L5(1) L3(I)▸L5(2) L5▸L4(I) END; approx(correlation(L4))▸r2 pCor(r2,N)(3)▸pr2 //rxy.z rp=(r0-r1*r2) rp=rp/(sqrt(1-r1^2)*sqrt(1-r2^2)) rp=approx(rp) ZCor(rp,N)(1)▸L0 L0(1)*SQRT(N-2)▸zrp prp=NORMALD_CDF(zrp) IF prp>0.5 THEN prp=1-prp END; prp2=2*prp //pCor(rp,N)(3)▸p //df,rxy,p2,rxz,p2,ryz,p2,rxy.z,p2 df,[r0,pr0],[r1,pr1],[r2,pr2],[rp,prp] END; #end // PRM1.pas //PRM1(n perm)/D.G.SCHRAUSSER/2025 //e.g.PRM1(5)/permutation vector (p)n from L1 #cas PRM1(N):= BEGIN //L1(N) provided {}▸L0 {}▸L2 FOR A FROM 1 TO N DO {RANDOM(),L1(A)}▸L0(A) END; // sort(L0)▸L2 FOR A FROM 1 TO N DO L2(A)▸L8;L8(2)▸L2(A) END; // L2 END; #end // PRM2.pas //PRM2(elements n)/D.G.SCHRAUSSER/2025 //Complete permutation matrix (P)n of elements n to 1 class, //where P=n! //e.g.PRM2(3) #cas PRM2(n):= BEGIN MAKELIST(1,P,1,n+1)▸L1 P=PERM(n,n) Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 50 0▸L1(1) {}▸L2 0▸M1 1▸J 0▸I 0▸SW // WHILE I≠n AND L1(I)≤n DO FOR I FROM 1 TO n DO IF I=1 THEN L1(1)+1▸L1(1) END; IF I=n AND L1(I)>n THEN BREAK END; IF L1(I)>n THEN 1▸L1(I);L1(I+1)+1▸L1(I+1) END; END;//I // FOR K FROM 1 TO n DO FOR L FROM K+1 TO n DO IF L1(K)=L1(L) THEN 1▸SW BREAK; END; END; END; IF SW=0 THEN SUPPRESS(L1,n+1)▸L2(J);J+1▸J END; 0▸SW END;//while // L2▸M1 IF n=2 THEN M1=[[1,2],[2,1]] M1▸L2 END; // P,M1 END; #end // PRM3.pas //PRM3(elements n, class m)/D.G.SCHRAUSSER/2025 //Complete permutation matrix w(P)n(km,kn-m) of n elements to class m, where P=n!/IIki!;n>=m //equivalent to combination without repetition Cn(m) //e.g.PRM3(6,3)[PRM3a] #cas PRM3(n,m):= BEGIN MAKELIST(1,P,1,n+1)▸L1 0▸L1(1) {}▸L2 0▸M1 1▸J 0▸I 0▸SW // WHILE I≠m AND L1(I)<n DO FOR I FROM 1 TO m DO IF I=1 THEN L1(1)+1▸L1(1) END; IF I=m AND L1(I)>n THEN BREAK END; IF L1(I)>n THEN 1▸L1(I) L1(I+1)+1▸L1(I+1) END; END;//I Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 51 // FOR K FROM 1 TO m DO FOR L FROM K+1 TO m DO IF L1(K)=L1(L) OR L1(K)>L1(L) THEN //<--- 1▸SW END; END; END; IF SW=0 THEN SUPPRESS(L1,n+1)▸L2(J) J+1▸J END; 0▸SW END;//while // //L2▸M1 PRM3a(n,m)// END; #end // PRM3a.pas //PRM3a(elements n,class m)/D.G.SCHRAUSSER/2025 //e.g.PRM3a(6,3) #cas PRM3a(N,M):= BEGIN {}▸L3 COMB(N,M)▸P MAKELIST(x+1-1,x,1,N)▸L1 // FOR J FROM 1 TO P DO FOR I FROM 1 TO M DO L2(J,I)▸L3(I) END; L3▸L4(J)▸M1 END; FOR I FROM 1 TO P DO L4(I)▸L5;DIFFERENCE(L5,L1)▸L7(I) END; FOR I FROM 1 TO P DO CONCAT(L4(I),L7(I))▸L8(I) END; L4▸L2;L8▸L3 {}▸L4 {}▸L8 {}▸L5 {}▸L6 {}▸L7 L3▸M2 P,M2 END; #end // PRM4.pas //PRM4(elements n, class m)/D.G.SCHRAUSSER/2025 //variation matrix w(V)n(m), where V=n^m;n>=m //e.g.PRM4(4,2)[PRM4a] #cas PRM4(n,m):= BEGIN MAKELIST(1,P,1,n+1)▸L1 0▸L1(1) {}▸L2 0▸M1 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 52 1▸J 0▸I 0▸SW // WHILE I≠m AND L1(I)<n DO FOR I FROM 1 TO m DO IF I=1 THEN L1(1)+1▸L1(1) END; IF I=m AND L1(I)>n THEN BREAK END; IF L1(I)>n THEN 1▸L1(I) L1(I+1)+1▸L1(I+1) END; END;//I // SUPPRESS(L1,n+1)▸L2(J);J+1▸J END;//while // //L2▸M1 PRM4a(n,m) END; #end // PRM4a.pas //PRM4a(elements n, class m)/D.G.SCHRAUSSER/2025 //e.g.PRM4a(4,3) #cas PRM4a(N,M):= BEGIN //L2 provided V=N^M X=M+1 FOR I FROM 1 TO V DO L2(I)▸L3 SUPPRESS(L3,X,N)▸L4(I) END; L4▸M1 V,M1 END; #end // PRM5.pas //PRM5(cases m)/D.G.SCHRAUSSER/2025 //variation matrix w(V)2(m) for paired 2 sample design PV_, //where V=2^m //e.g.PRM5(3) #cas PRM5(N):= BEGIN M1=0 2^N▸P X=−1 0▸Z P/2▸A // FOR I FROM 1 TO N DO FOR J FROM 1 TO P DO X▸M1(J,I) Z=Z+1 IF Z=A THEN X=X*−1;0▸Z; END; END; 0▸Z // A=A/2 // A=A*0.5 END; // Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 53 M1▸L3 P,M1 END; #end // PRMDAT.pas //PRMDAT(rows n, cols k)/D.G.SCHRAUSSER/2025 //e.g.PRMDAT(720,6) #cas PRMDAT(N,K):= BEGIN //L3 provided FOR J FROM 1 TO N DO FOR I FROM 1 TO K DO L3(M1(J,I))▸M2(J,I) END; END; END; #end // Q Q01_.pas //Q01_()/D.G.SCHRAUSSER/2025 //Statistical parameters 1.0 //[L1:Raw] //L2:Distribution //L3:z-value //L4:z´-value #cas Q01_():= BEGIN //L1 provided SORT(L1)▸L2 //distr SIZE(L1)▸N mean(L1)▸AM stddev(L1)▸SD stddevp(L1)▸SD1 variance(L1)▸VA VA1=VA*(N/(N-1)) //SD1^2 SEM=sqrt((VA1/N)) VQ=SD/AM QGM= N NTHROOT(product(L1)) QHM=N/Σ(1/L1) approx(MAKELIST(((L2(X)-AM)/SD),X,1,N))▸L3 //z approx(MAKELIST(((L2(X)-AM)/SD1),X,1,N))▸L4 //z´ // approx(N,[AM,SEM],SD,SD1,VA,VA1,VQ,[QGM,QHM]) END; #end // Q02_.pas //Q02_()/D.G.SCHRAUSSER/2025 //Statistical parameters 2.0 //[L1:Raw] //L2:Distribution //L3:z-value #cas Q02_():= BEGIN //L1 provided Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 54 SORT(L1)▸L2 // SIZE(L1)▸N mean(L1)▸AM stddev(L1)▸SD stddevp(L1)▸SD1 approx(MAKELIST(((L2(X)-AM)/SD),X,1,N))▸L3 // Σ(L3.^3)/N▸A3 sqrt(6/N)▸SA3 Σ(L3.^4)/N-3▸A4 2*SA3▸SA4 Σ((L1 .- AM) .^ 3)*N/((N-1)*(N-2)*SD1^3)▸A31 A41=((N-1)*(N-2)*(N-3)*SD1^4) EX1=Σ((L1 .- AM) .^ 4)*N*(N+1) EX2=Σ((L1 .- AM) .^ 2) EX2=3*EX2*EX2*(N-1) A41=(EX1-EX2)/A41 NORMALD_CDF(A3/SA3)▸PA3 P2A3=2*PA3 IF PA3>0.5 THEN P2A3=2*(1-PA3) END; NORMALD_CDF(A4/SA4)▸PA4 P2A4=2*PA4 IF PA4>0.5 THEN P2A4=2*(1-PA4) END; // approx(N,[A3,A31],A3/SA3,[P2A3],[A4,A41],A4/SA4,[P2A4]) END; #end // R rDiff.pas //rDiff(r1,n1,r2,n2)/D.G.SCHRAUSSER/2025 //e.g.rDiff(0.78,12,0.34,8)[ZCor] #cas rDiff(R1,N1,R2,N2):= BEGIN ZCor(R1,N1)(1)▸L2 L2(1)▸L1(1) ZCor(R2,N2)(1)▸L2 L2(1)▸L1(2) L1(1)-L1(2)▸L2(1) sqrt((1/(N1-3))+1/(N2-3))▸L2(2) L2(1)/L2(2)▸L2(3) NORMALD_CDF(L2(3))▸L2(4) 1-L2(4)▸L2(5) 2*L2(5)▸L2(6) IF L2(5)>0.5 THEN 2*L2(4)▸L2(6) END; //Zd,sZd,z,p,1-p,p2 [L2(1),L2(2)],[L2(3)],L2(4),L2(5),[L2(6)] END; #end // RHO.pas //RHO()/D.G.SCHRAUSSER/2025 //Spearman's rank correlation coefficient rho rs/[pCor] #cas RHO():= BEGIN //L1()(2) provided size(L1)▸N Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 61 AvSk(A0,S steps k),e.g.AvSk(100,3) A*((2) NTHROOT (2))^K AvTv(Av0,Tv0,Tv) A*e^(0.5*LN((T/B))) AvTvk(Av0,Tv steps k),e.g.AvTvk(8,-3) A*(√2^K) B BINOM(a,b) Σ(((A+B)!/(I!*(A+B-I)!))*2.000^(-I)*2.000^(-(A+BI)),I,0.000,A) C Cf2(R)‘Cohen’s f²’ R^2/(1-R^2) Ch(p1,p2)‘Cohen’s h for proportion differences’ 2*ASIN(√A)-2*ASIN(√B) ChA(p2,h) SIN((1/2)*(2*ASIN(√B)+H))^2 ChB(p1,h) (-SIN((1/2)*(-2*ASIN(√A)+H)))^2 CIr(P,S,R),CIr(ci%,sdx or sdy,rxy),e.g.CIr(0.99,0.342,0.98) NORMALD_CDF(1-(1-P)/2)*S*√(1-R^2) CIx [CIx(B,C,A),CIx(n,ci%,sd),e.g.6.7+CIx(10,0.99,1.676)] STUDENT_ICDF(B-1,1-((1-C)/2))*√((A^2)*(B/(B-1))/B) D D2R(deg) X/180.000*π Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 62 E EFG(x1,L1)‘epsilon, Cohen’s d’ (A-mean(L1))/stddevp(L1) EFR(x1,L1,R)‘epsilon, Cohen’s d for paired samples’ ((A-mean(L1))/stddevp(L1))/√(1-R) Ev(Tv,Av)‘exposure value’ (LN(2))^(-1)*LN(T*A^2) F FMCORR(R,n) A^2.000*(B-4.000)/(3.000*(-(A^2.000)+1.000)) H HM_[e.g.HM_(L2)] SIZE(L1)/Σ((L1(B))^(-1),B,1,SIZE(L1)) I ISOA(iso°) 10^(0.1*(S-1)) ISOL(iso) (10*LN(S)/LN(10))+1 M MCORR(r1,r2,r3) √((A^2.000+B^2.000-2.000*C*A*B)/(1.000-C^2.000)) mr(r1,n1,r2,n2) (e^(2*(((0.5*LN(((1+A)/(1-A)))*(B-3))+(0.5*LN(((1+C)/(1C)))*(D-3)))/((B-3)+(D-3))))-1)/(e^(2*(((0.5*LN(((1+A)/(1A)))*(B-3))+(0.5*LN(((1+C)/(1-C)))*(D-3)))/((B-3)+(D-3))))+1) Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 63 mZ(r1,n1,r2,n2) ((0.5*LN(((1+A)/(1-A)))*(B-3))+(0.5*LN(((1+C)/(1-C)))*(D3)))/((B-3)+(D-3)) N NBINOM(k,p,n) Σ(((K+I-1.000)!/(I!*(K-1.000)!))*P^K*(1.000-P)^I,I,0.000,N-K) nk(N,K) N!/(K!*(N-K)!) npz(x,am,sd,N)‘p>=z quantity at N’,e.g.npz(160,100,15,8*10^9) (1-NORMALD_CDF(((X-A)/S)))*N P p2F(a,b) (1-CHISQUARE_CDF(1,((A-((A+B)/2))^2/((A+B)/2))+((B- ((A+B)/2))^2/((A+B)/2))))/2 p4F(a,b,c,d) (1-CHISQUARE_CDF(1,((A+B+C+D)*(A*DB*C)^2/((A+B)*(C+D)*(A+C)*(B+D)))))/2 p4FY(a,b,c,d) Yates corr 4<fe<7 (1-CHISQUARE_CDF(1,((A+B+C+D)*(ABS(A*D-B*C)- ((A+B+C+D)/2))^2/((A+B)*(C+D)*(A+C)*(B+D)))))/2 PHI(a,d,b,c) (A*D-B*C)/(sqrt((A+C)*(B+D)*(A+B)*(C+D))) pMCORR(n,R) (1-FISHER_CDF(3,(B-4),(A^2*(B-4)/(3*(-(A^2)+1)))))/2 pMN(b,c) (1-CHISQUARE_CDF(1,((A-B)^2/(A+B))))/2 pMNY(b,c) Yates corr 20<b+c<30 (1-CHISQUARE_CDF(1,((ABS(A-B)-0.5)^2/(A+B))))/2 POL(x) polar_coordinates(X) Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 64 pPHI(a,d,b,c) (1-CHISQUARE_CDF(1,((A*DB*C)/(√((A+C)*(B+D)*(A+B)*(C+D))))^2*(A+B+C+D)))/2 prbis(L1,L2) normald_cdf((((mean(L1)- mean(L2))/stddev(CONCAT(L1,L2)))*SIZE(L1)*SIZE(L2)/((1/(√(2*π) ))*e^(- (NORMALD_ICDF((SIZE(L2)/SIZE(CONCAT(L1,L2))))^2)/2)*SIZE(CONCA T(L1,L2))^2))/(√(SIZE(L1)*SIZE(L2))/((√SIZE(CONCAT(L1,L2))*SIZ E(CONCAT(L1,L2))*1/(√(2*π)))*e^(- (NORMALD_ICDF((SIZE(L2)/SIZE(CONCAT(L1,L2))))^2)/2)))) prbisR(L1,L2) normald_cdf(((size(L1)*size(L2)+(((size(L1))^2+size(L1))/2)- ΣLIST(L1)- size(L1)*size(L2)/2)/(sqrt(size(L1)*size(L2)*(size(L1)+size(L2 )+1)/12)))) prr(r1,r2,n1,n2) NORMALD_CDF(((0.5*LN(((1+A)/(1-A)))-0.5*LN(((1+B)/(1B))))/(√((1/(C-3))+1/(D-3))))) prtet(b,c,a,d) NORMALD_CDF((COS((π/(1+√(B*C/(A*D)))))/(√(((A+B)/(A+B+C+D))*(( A+C)/(A+B+C+D))*((C+D)/(A+B+C+D))*((B+D)/(A+B+C+D))/(A+B+C+D)) *(1/(((1/(√(2*π)))*e^(- (NORMALD_ICDF(((C+D)/(A+B+C+D)))^2)/2))*((1/(√(2*π)))*e^(- (NORMALD_ICDF(((B+D)/(A+B+C+D)))^2)/2))))))) pRW(L1,L2) STUDENT_CDF(SIZE(L1)-2,((correlation(L1,L2)*√(SIZE(L1)- 2))/(√(1-correlation(L1,L2)^2)))) pRWx(n,r) STUDENT_CDF(B-2,((A*√(B-2))/(√(1-A^2)))) prxy_z(rxy_z,n) NORMALD_CDF(0.5*LN(((1+A)/(1-A)))*√(B-2)) PTG(a,b) √(A^2+B^2) pTKV(L1,L2) STUDENT_CDF(SIZE(L1)+SIZE(L2)-2,(((variance(L1)- variance(L2))*√(SIZE(L1)- 2))/(2*√(variance(L1)*variance(L2)*(1-correlation(L1,L2)))))) Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 65 pTT_(L1,y) STUDENT_CDF(SIZE(L1)-1,((mean(L1)- A)/(√(stddev(L1)^2/(SIZE(L1)-1))))) pTU_(L1,L2) STUDENT_CDF(SIZE(L1)+SIZE(L2)-2,(mean(L1)- mean(L2))/(√((ΣLIST(MAKELIST((L1(A)- mean(L1))^2,A,1,SIZE(L1)))+ΣLIST(MAKELIST((L2(A)- mean(L2))^2,A,1,SIZE(L2))))/(SIZE(L1)-1+SIZE(L2)- 1))*(√(1/SIZE(L1))+√(1/SIZE(L2))))) pTUX(n1,n2,x1,x2,s21,s22) STUDENT_CDF(D+F-2,((A-B)/(√((C*D+E*F)/(D-1+F1))*(√(1/D)+√(1/F))))) pTV_(L1) student_cdf(size(L1)-1,ΣLIST(MAKELIST(L1(A)- (L2(A)),A,1,size(L1)))/(size(L1))/(√((ΣLIST(MAKELIST((L1(A)- (L2(A)))^2,A,1,size(L1)))-ΣLIST(MAKELIST(L1(A)- (L2(A)),A,1,size(L1)))^2/(size(L1)))/(size(L1)- 1))*1/(√(size(L1)-1)))) pz4F(a,b,c,d)[e.g.pz4F(11,20,80,58)] NORMALD_CDF(((D- (A+B+C+D)*((D+B)*(C+D)/(A+B+C+D)^2))/(√((A+B+C+D)*(1- ((D+B)*(C+D)/(A+B+C+D)^2))-(A+B+C+D)*(A+B+C+D1)*((D+B)*(C+D)/(A+B+C+D)^2)*(((D+B)*(C+D)/(A+B+C+D)^2)-((D+B1)*(C+D-1)/(A+B+C+D-1)^2)))))) pzBN(a,b) NORMALD_CDF(((A-(A+B)/2)/(√((A+B)/4)))) R R2D(rad) X/π*180.000 rbis(L1,L2) ((mean(L1)- mean(L2))/stddev(CONCAT(L1,L2)))*SIZE(L1)*SIZE(L2)/((1/(√(2*π) ))*e^(- (NORMALD_ICDF((SIZE(L2)/SIZE(CONCAT(L1,L2))))^2)/2)*SIZE(CONCA T(L1,L2))^2) rbisR(L1,L2) (2/(SIZE(L1)+SIZE(L2)))*(mean(L1)-mean(L2)) Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 66 RED(r) A^2*100 RND1(n) MAKELIST(RANDNORM,A,1,B) RND2(n) MAKELIST(RANDOM,A,1,B) rpbis(L1,L2) (mean(L1)- mean(L2))/stddev(CONCAT(L1,L2))*√(SIZE(L1)*SIZE(L2)/(SIZE(CONC AT(L1,L2)))^2) rxy(x1,x2) approx(correlation(L1,L2)) rtet(b,c,a,d),rad COS((π/(1+√(B*C/(A*D))))) rxy_z(rxy,rxz,ryz) (A-B*C)/(√(1-B^2)*√(1-C^2)) ry_xz(rxy,rxz,ryz) (A-B*C)/(sqrt(1-B^2)) rZ(Z) (e^(2*A)-1)/(e^(2*A)+1) S SCR(n,k,R) 1.00-((A-3.00)/(A-B-2.00))*((1.00-C^2.00)+((2.00/(AB)))*(1.00-C^2.00)^2.00) SMG [SMG(A,B),SMG(sd,n)] √((A^2)*(B/(B-1))/B) SQR(x) A^2 srbis(L1,L2) √(SIZE(L1)*SIZE(L2))/((√SIZE(CONCAT(L1,L2))*SIZE(CONCAT(L1,L2) )*1/(√(2*π)))*e^(- (NORMALD_ICDF((SIZE(L2)/SIZE(CONCAT(L1,L2))))^2)/2)) Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 67 srtet(b,c,a,d) √(((A+B)/(A+B+C+D))*((A+C)/(A+B+C+D))*((C+D)/(A+B+C+D))*((B+D) /(A+B+C+D))/(A+B+C+D))*(1/(((1/(√(2*π)))*e^(- (NORMALD_ICDF(((C+D)/(A+B+C+D)))^2)/2))*((1/(√(2*π)))*e^(- (NORMALD_ICDF(((B+D)/(A+B+C+D)))^2)/2)))) sumd2(L1) ΣLIST(MAKELIST((L1(A)-(L2(A)))^2,A,1,SIZE(L1))) CAS input L4:=ΣLIST(L3:=MAKELIST((L1(x)-(L2(x)))^2,x,1,size(L1))) L4:=ΣLIST(L3:=MAKELIST(L1(x)-(L2(x)),x,1,size(L1))) L4:=ΣLIST(L3:=MAKELIST(L1(x)-(L2(x)),x,1,size(L1)))^2 sumx2(L1,L2) CAS input ΣLIST(L3:=approx(MAKELIST((L1(x)-mean(L1))^2,x,1,size(L1)))) T TEv(Ev,Av) 2^E/A^2 tr(r,n) (R*√(N-2))/(√(1-R^2)) TRW(L1,L2) (correlation(L1,L2)*√(SIZE(L1)-2))/(√(1-correlation(L1,L2)^2)) tTKV(L1,L2) ((variance(L1)-variance(L2))*sqrt(size(L1)- 2))/(2*sqrt(variance(L1)*variance(L2)*(1-correlation(L1,L2)))) tTT_(L1,y) (mean(L1)-A)/(√(stddev(L1)^2/(SIZE(L1)-1))) tTU_(L1,L2) (mean(L1)-mean(L2))/(sqrt((ΣLIST(MAKELIST((L1(x)- mean(L1))^2,x,1,size(L1)))+ ΣLIST(MAKELIST((L2(x)- mean(L2))^2,x,1,size(L2))))/ (size(L1)-1+size(L2)- 1))*(sqrt(1/size(L1))+sqrt(1/size(L2)))) tTUX(x1,x2,s21,n1,s22,n2) (A-B)/(√((C*D+E*F)/(D-1+F-1))*(√(1/D)+√(1/F))) tTV_(L1) ΣLIST(MAKELIST(L1(A)- (L2(A)),A,1,size(L1)))/(size(L1))/(√((ΣLIST(MAKELIST((L1(A)- Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 68 (L2(A)))^2,A,1,size(L1)))-ΣLIST(MAKELIST(L1(A)- (L2(A)),A,1,size(L1)))^2/(size(L1)))/(size(L1)- 1))*1/(√(size(L1)-1))) U U_1(L1,L2) SIZE(L1)*SIZE(L2)+(((SIZE(L1))^2+SIZE(L1))/2)-ΣLIST(L1) U_2(L1,L2) SIZE(L1)*SIZE(L2)+(((SIZE(L2))^2+SIZE(L2))/2)-ΣLIST(L2) X x2F(a,b) ((A-((A+B)/2))^2/((A+B)/2))+(B-((A+B)/2))^2/((A+B)/2) x4F(a,b,c,d) (A+B+C+D)*(A*D-B*C)^2/((A+B)*(C+D)*(A+C)*(B+D)) x4FY(a,b,c,d) Yates corr 4<fe<7 (A+B+C+D)*(ABS(A*D-B*C)- ((A+B+C+D)/2))^2/((A+B)*(C+D)*(A+C)*(B+D)) xMN(b,c) (A-B)^2/(A+B) xMNY(b,c) Yates corr 20<b+c<30 (ABS(A-B)-0.5)^2/(A+B) xPHI(a,d,b,c) (((A*D-B*C)/(√((A+C)*(B+D)*(A+B)*(C+D)))))^2*(A+B+C+D) Z z4F(a,b,c,d) (D-(A+B+C+D)*((D+B)*(C+D)/(A+B+C+D)^2))/(√((A+B+C+D)*(1- ((D+B)*(C+D)/(A+B+C+D)^2))-(A+B+C+D)*(A+B+C+D1)*((D+B)*(C+D)/(A+B+C+D)^2)*(((D+B)*(C+D)/(A+B+C+D)^2)-((D+B1)*(C+D-1)/(A+B+C+D-1)^2)))) zBN(a,b) (A-(A+B)/2)/(√((A+B)/4)) Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 69 Zr(r) 0.5*LN((1+A)/(1-A)) zrbis(L1,L2) (((mean(L1)- mean(L2))/stddev(CONCAT(L1,L2)))*SIZE(L1)*SIZE(L2)/((1/(√(2*π) ))*e^(- (NORMALD_ICDF((SIZE(L2)/SIZE(CONCAT(L1,L2))))^2)/2)*SIZE(CONCA T(L1,L2))^2))/(√(SIZE(L1)*SIZE(L2))/((√SIZE(CONCAT(L1,L2))*SIZ E(CONCAT(L1,L2))*1/(√(2*π)))*e^(- (NORMALD_ICDF((SIZE(L2)/SIZE(CONCAT(L1,L2))))^2)/2))) zrbisR(L1,L2) (size(L1)*size(L2)+(((size(L1))^2+size(L1))/2)-ΣLIST(L1)- size(L1)*size(L2)/2)/(sqrt(size(L1)*size(L2)*(size(L1)+size(L2 )+1)/12)) zrr(r1,r2,n1,n2) (0.5*LN((1+A)/(1-A))-0.5*LN((1+B)/(1-B)))/(√(1/(C-3)+1/(D-3))) zrxy_z(rxy_z,n) 0.5*LN(((1+A)/(1-A)))*√(B-2) ZWERT(x1,x,s) (A-B)/C zVAL(L1),e.g.L2:=zVAL(L1) approx(MAKELIST(((L1(X)-mean(L1))/stddev(L1)),X,1,SIZE(L1))) zVALp(L1),e.g.L3:=zVAL(L1) approx(MAKELIST(((L1(X)-mean(L1))/stddevp(L1)),X,1,SIZE(L1))) Application functions Function To select: F01.pas //F01()/D.G.SCHRAUSSER/2022 //Function: Equations 1.0 EXPORT F01() BEGIN "√(1-((X-W)/A)^2)*A+V"▸F1; "−√(1-((X-W)/A)^2)*A+V"▸F2; "√(1-((X-T)/B)^2)*B+U"▸F3; "-√(1-((X-T)/B)^2)*B+U"▸F4; "√(1-((X-R)/C)^2)*C+S"▸F5; Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 70 "-√(1-((X-R)/C)^2)*C+S"▸F6; 200▸A; 150▸B; 344▸C; 1▸W; 450▸T; 1000▸R; "Function: Equations 1.0" END; // F02.pas //F02()/D.G.SCHRAUSSER/2022 //Function: Equations 2.0 EXPORT F02() BEGIN "NORMALD_CDF(0,1,X)"▸F1; "NORMALD(0,1,X)"▸F2; "STUDENT(50,X)"▸F3; "STUDENT_CDF(50,X)"▸F4; "CHISQUARE(1,X)"▸F5; "CHISQUARE_CDF(1,X)"▸F6; "FISHER_CDF(25,3,X)"▸F7; "FISHER(25,3,X)"▸F8; "0"▸F9; "0"▸F0; "Function: Equations 2.0" END; // F03.pas //F03()/D.G.SCHRAUSSER/2025 //Function: Equations 3.0 //F3-7:Derivatives of the standard normal distribution function, f'(z)- f'''''(z) EXPORT F03() BEGIN "NORMALD_CDF(0,1,X)"▸F1; "NORMALD(0,1,X)"▸F2; "∂((1/√(2*π))*e^((-1/2)*X^2),X=X)"▸F3; "∂(∂((1/√(2*π))*e^((-1/2)*X^2),X),X)"▸F4; "∂(∂(∂((1/√(2*π))*e^((-1/2)*X^2),X),X),X)"▸F5; "∂(∂(∂(∂((1/√(2*π))*e^((-1/2)*X^2),X),X),X),X)"▸F6; "∂(∂(∂(∂(∂((1/√(2*π))*e^((-1/2)*X^2),X),X),X),X),X)"▸F7; "0"▸F8; "0"▸F9; "0"▸F0; "Function: Equations 3.0" END; // F04.pas //F04()/D.G.SCHRAUSSER/2025 //Function: Equations 4.0 //F3:Derivative of Gamma, f'(x) //F5-7:Derivatives of the exponential function, f(x)={f'(x)-f'''(x)...} EXPORT F04() BEGIN "CAS.Gamma(X)"▸F1; "(X)!"▸F2; "∂(Gamma(X),X=X)"▸F3; "EXP(X)"▸F4; Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 77 {1.,0.,0.,1.,0.,1.}▸L1 {0.,1.,0.,1.,0.,0.}▸L2 {1.,0.,0.,1.,0.,1.,1.,1.,1.,0.,0.,1.,0.,0.,0.,1.,1.,0.,1.,0.,0.,0.,0.,0.,1.} ▸L1 {0.,1.,0.,1.,0.,0.,1.,1.,1.,1.,0.,0.,1.,1.,0.,1.,1.,1.,0.,1.,1.,1.,0.,0.,1.} ▸L2 PV_ {{1.,4.},{2.,6.},{2.,7.}}▸L1 (Scambor, 1997; Scambor & Schrausser, 2022, p. 7) {{8.,9.},{2.,3.},{9.,7.},{2.,7.},{9.,8.}}▸L1 {{8.6,4.5},{9.2,4.1},{6.7,1.2},{9.6,4.5},{6.2,7.6},{6.1,8.5},{9.3,4.2},{7.3, 8.2}}▸L1 PU_ {18.,30.,54.}▸L1 {6.,12.}▸L2 (Schrausser, 1996, 2022b, p. 2) {18.04,10.07,22.27,1.96,18.88,12.81,3.08,21.49,1.96,24.93}▸L1 {24.96,22.39}▸L2 (Schrausser, 1997, 1998a) Matrices wP8_4_4.dat M1=[[1,2,3,4,5,6,7,8],[1,2,3,5,4,6,7,8],[1,2,4,5,3,6,7,8],[1,3,4,5,2,6,7,8],[2,3,4,5, 1,6,7,8],[1,2,3,6,4,5,7,8],[1,2,4,6,3,5,7,8],[1,3,4,6,2,5,7,8],[2,3,4,6,1,5,7,8],[1,2 ,5,6,3,4,7,8],[1,3,5,6,2,4,7,8],[2,3,5,6,1,4,7,8],[1,4,5,6,2,3,7,8],[2,4,5,6,1,3,7,8] ,[3,4,5,6,1,2,7,8],[1,2,3,7,4,5,6,8],[1,2,4,7,3,5,6,8],[1,3,4,7,2,5,6,8],[2,3,4,7,1,5 ,6,8],[1,2,5,7,3,4,6,8],[1,3,5,7,2,4,6,8],[2,3,5,7,1,4,6,8],[1,4,5,7,2,3,6,8],[2,4,5, 7,1,3,6,8],[3,4,5,7,1,2,6,8],[1,2,6,7,3,4,5,8],[1,3,6,7,2,4,5,8],[2,3,6,7,1,4,5,8],[1 ,4,6,7,2,3,5,8],[2,4,6,7,1,3,5,8],[3,4,6,7,1,2,5,8],[1,5,6,7,2,3,4,8],[2,5,6,7,1,3,4, 8],[3,5,6,7,1,2,4,8],[4,5,6,7,1,2,3,8],[1,2,3,8,4,5,6,7],[1,2,4,8,3,5,6,7],[1,3,4,8,2 ,5,6,7],[2,3,4,8,1,5,6,7],[1,2,5,8,3,4,6,7],[1,3,5,8,2,4,6,7],[2,3,5,8,1,4,6,7],[1,4, 5,8,2,3,6,7],[2,4,5,8,1,3,6,7],[3,4,5,8,1,2,6,7],[1,2,6,8,3,4,5,7],[1,3,6,8,2,4,5,7], [2,3,6,8,1,4,5,7],[1,4,6,8,2,3,5,7],[2,4,6,8,1,3,5,7],[3,4,6,8,1,2,5,7],[1,5,6,8,2,3, 4,7],[2,5,6,8,1,3,4,7],[3,5,6,8,1,2,4,7],[4,5,6,8,1,2,3,7],[1,2,7,8,3,4,5,6],[1,3,7,8 ,2,4,5,6],[2,3,7,8,1,4,5,6],[1,4,7,8,2,3,5,6],[2,4,7,8,1,3,5,6],[3,4,7,8,1,2,5,6],[1, 5,7,8,2,3,4,6],[2,5,7,8,1,3,4,6],[3,5,7,8,1,2,4,6],[4,5,7,8,1,2,3,6],[1,6,7,8,2,3,4,5 ],[2,6,7,8,1,3,4,5],[3,6,7,8,1,2,4,5],[4,6,7,8,1,2,3,5],[5,6,7,8,1,2,3,4]] L1={{1,2,3,4,5,6,7,8},{1,2,3,5,4,6,7,8},{1,2,4,5,3,6,7,8},{1,3,4,5,2,6,7,8},{2,3,4,5, 1,6,7,8},{1,2,3,6,4,5,7,8},{1,2,4,6,3,5,7,8},{1,3,4,6,2,5,7,8},{2,3,4,6,1,5,7,8},{1,2 ,5,6,3,4,7,8},{1,3,5,6,2,4,7,8},{2,3,5,6,1,4,7,8},{1,4,5,6,2,3,7,8},{2,4,5,6,1,3,7,8} ,{3,4,5,6,1,2,7,8},{1,2,3,7,4,5,6,8},{1,2,4,7,3,5,6,8},{1,3,4,7,2,5,6,8},{2,3,4,7,1,5 ,6,8},{1,2,5,7,3,4,6,8},{1,3,5,7,2,4,6,8},{2,3,5,7,1,4,6,8},{1,4,5,7,2,3,6,8},{2,4,5, 7,1,3,6,8},{3,4,5,7,1,2,6,8},{1,2,6,7,3,4,5,8},{1,3,6,7,2,4,5,8},{2,3,6,7,1,4,5,8},{1 ,4,6,7,2,3,5,8},{2,4,6,7,1,3,5,8},{3,4,6,7,1,2,5,8},{1,5,6,7,2,3,4,8},{2,5,6,7,1,3,4, 8},{3,5,6,7,1,2,4,8},{4,5,6,7,1,2,3,8},{1,2,3,8,4,5,6,7},{1,2,4,8,3,5,6,7},{1,3,4,8,2 ,5,6,7},{2,3,4,8,1,5,6,7},{1,2,5,8,3,4,6,7},{1,3,5,8,2,4,6,7},{2,3,5,8,1,4,6,7},{1,4, 5,8,2,3,6,7},{2,4,5,8,1,3,6,7},{3,4,5,8,1,2,6,7},{1,2,6,8,3,4,5,7},{1,3,6,8,2,4,5,7}, {2,3,6,8,1,4,5,7},{1,4,6,8,2,3,5,7},{2,4,6,8,1,3,5,7},{3,4,6,8,1,2,5,7},{1,5,6,8,2,3, 4,7},{2,5,6,8,1,3,4,7},{3,5,6,8,1,2,4,7},{4,5,6,8,1,2,3,7},{1,2,7,8,3,4,5,6},{1,3,7,8 ,2,4,5,6},{2,3,7,8,1,4,5,6},{1,4,7,8,2,3,5,6},{2,4,7,8,1,3,5,6},{3,4,7,8,1,2,5,6},{1, 5,7,8,2,3,4,6},{2,5,7,8,1,3,4,6},{3,5,7,8,1,2,4,6},{4,5,7,8,1,2,3,6},{1,6,7,8,2,3,4,5 },{2,6,7,8,1,3,4,5},{3,6,7,8,1,2,4,5},{4,6,7,8,1,2,3,5},{5,6,7,8,1,2,3,4}} Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 78 wP9_4_5.dat M1=[[1.,2.,3.,4.,5.,6.,7.,8.,9.],[1.,2.,3.,5.,4.,6.,7.,8.,9.],[1.,2.,4.,5.,3.,6.,7.,8 .,9.],[1.,3.,4.,5.,2.,6.,7.,8.,9.],[2.,3.,4.,5.,1.,6.,7.,8.,9.],[1.,2.,3.,6.,4.,5.,7. ,8.,9.],[1.,2.,4.,6.,3.,5.,7.,8.,9.],[1.,3.,4.,6.,2.,5.,7.,8.,9.],[2.,3.,4.,6.,1.,5., 7.,8.,9.],[1.,2.,5.,6.,3.,4.,7.,8.,9.],[1.,3.,5.,6.,2.,4.,7.,8.,9.],[2.,3.,5.,6.,1.,4 .,7.,8.,9.],[1.,4.,5.,6.,2.,3.,7.,8.,9.],[2.,4.,5.,6.,1.,3.,7.,8.,9.],[3.,4.,5.,6.,1. ,2.,7.,8.,9.],[1.,2.,3.,7.,4.,5.,6.,8.,9.],[1.,2.,4.,7.,3.,5.,6.,8.,9.],[1.,3.,4.,7., 2.,5.,6.,8.,9.],[2.,3.,4.,7.,1.,5.,6.,8.,9.],[1.,2.,5.,7.,3.,4.,6.,8.,9.],[1.,3.,5.,7 .,2.,4.,6.,8.,9.],[2.,3.,5.,7.,1.,4.,6.,8.,9.],[1.,4.,5.,7.,2.,3.,6.,8.,9.],[2.,4.,5. ,7.,1.,3.,6.,8.,9.],[3.,4.,5.,7.,1.,2.,6.,8.,9.],[1.,2.,6.,7.,3.,4.,5.,8.,9.],[1.,3., 6.,7.,2.,4.,5.,8.,9.],[2.,3.,6.,7.,1.,4.,5.,8.,9.],[1.,4.,6.,7.,2.,3.,5.,8.,9.],[2.,4 .,6.,7.,1.,3.,5.,8.,9.],[3.,4.,6.,7.,1.,2.,5.,8.,9.],[1.,5.,6.,7.,2.,3.,4.,8.,9.],[2. ,5.,6.,7.,1.,3.,4.,8.,9.],[3.,5.,6.,7.,1.,2.,4.,8.,9.],[4.,5.,6.,7.,1.,2.,3.,8.,9.],[ 1.,2.,3.,8.,4.,5.,6.,7.,9.],[1.,2.,4.,8.,3.,5.,6.,7.,9.],[1.,3.,4.,8.,2.,5.,6.,7.,9.] ,[2.,3.,4.,8.,1.,5.,6.,7.,9.],[1.,2.,5.,8.,3.,4.,6.,7.,9.],[1.,3.,5.,8.,2.,4.,6.,7.,9 .],[2.,3.,5.,8.,1.,4.,6.,7.,9.],[1.,4.,5.,8.,2.,3.,6.,7.,9.],[2.,4.,5.,8.,1.,3.,6.,7. ,9.],[3.,4.,5.,8.,1.,2.,6.,7.,9.],[1.,2.,6.,8.,3.,4.,5.,7.,9.],[1.,3.,6.,8.,2.,4.,5., 7.,9.],[2.,3.,6.,8.,1.,4.,5.,7.,9.],[1.,4.,6.,8.,2.,3.,5.,7.,9.],[2.,4.,6.,8.,1.,3.,5 .,7.,9.],[3.,4.,6.,8.,1.,2.,5.,7.,9.],[1.,5.,6.,8.,2.,3.,4.,7.,9.],[2.,5.,6.,8.,1.,3. ,4.,7.,9.],[3.,5.,6.,8.,1.,2.,4.,7.,9.],[4.,5.,6.,8.,1.,2.,3.,7.,9.],[1.,2.,7.,8.,3., 4.,5.,6.,9.],[1.,3.,7.,8.,2.,4.,5.,6.,9.],[2.,3.,7.,8.,1.,4.,5.,6.,9.],[1.,4.,7.,8.,2 .,3.,5.,6.,9.],[2.,4.,7.,8.,1.,3.,5.,6.,9.],[3.,4.,7.,8.,1.,2.,5.,6.,9.],[1.,5.,7.,8. ,2.,3.,4.,6.,9.],[2.,5.,7.,8.,1.,3.,4.,6.,9.],[3.,5.,7.,8.,1.,2.,4.,6.,9.],[4.,5.,7., 8.,1.,2.,3.,6.,9.],[1.,6.,7.,8.,2.,3.,4.,5.,9.],[2.,6.,7.,8.,1.,3.,4.,5.,9.],[3.,6.,7 .,8.,1.,2.,4.,5.,9.],[4.,6.,7.,8.,1.,2.,3.,5.,9.],[5.,6.,7.,8.,1.,2.,3.,4.,9.],[1.,2. ,3.,9.,4.,5.,6.,7.,8.],[1.,2.,4.,9.,3.,5.,6.,7.,8.],[1.,3.,4.,9.,2.,5.,6.,7.,8.],[2., 3.,4.,9.,1.,5.,6.,7.,8.],[1.,2.,5.,9.,3.,4.,6.,7.,8.],[1.,3.,5.,9.,2.,4.,6.,7.,8.],[2 .,3.,5.,9.,1.,4.,6.,7.,8.],[1.,4.,5.,9.,2.,3.,6.,7.,8.],[2.,4.,5.,9.,1.,3.,6.,7.,8.], [3.,4.,5.,9.,1.,2.,6.,7.,8.],[1.,2.,6.,9.,3.,4.,5.,7.,8.],[1.,3.,6.,9.,2.,4.,5.,7.,8. ],[2.,3.,6.,9.,1.,4.,5.,7.,8.],[1.,4.,6.,9.,2.,3.,5.,7.,8.],[2.,4.,6.,9.,1.,3.,5.,7., 8.],[3.,4.,6.,9.,1.,2.,5.,7.,8.],[1.,5.,6.,9.,2.,3.,4.,7.,8.],[2.,5.,6.,9.,1.,3.,4.,7 .,8.],[3.,5.,6.,9.,1.,2.,4.,7.,8.],[4.,5.,6.,9.,1.,2.,3.,7.,8.],[1.,2.,7.,9.,3.,4.,5. ,6.,8.],[1.,3.,7.,9.,2.,4.,5.,6.,8.],[2.,3.,7.,9.,1.,4.,5.,6.,8.],[1.,4.,7.,9.,2.,3., 5.,6.,8.],[2.,4.,7.,9.,1.,3.,5.,6.,8.],[3.,4.,7.,9.,1.,2.,5.,6.,8.],[1.,5.,7.,9.,2.,3 .,4.,6.,8.],[2.,5.,7.,9.,1.,3.,4.,6.,8.],[3.,5.,7.,9.,1.,2.,4.,6.,8.],[4.,5.,7.,9.,1. ,2.,3.,6.,8.],[1.,6.,7.,9.,2.,3.,4.,5.,8.],[2.,6.,7.,9.,1.,3.,4.,5.,8.],[3.,6.,7.,9., 1.,2.,4.,5.,8.],[4.,6.,7.,9.,1.,2.,3.,5.,8.],[5.,6.,7.,9.,1.,2.,3.,4.,8.],[1.,2.,8.,9 .,3.,4.,5.,6.,7.],[1.,3.,8.,9.,2.,4.,5.,6.,7.],[2.,3.,8.,9.,1.,4.,5.,6.,7.],[1.,4.,8. ,9.,2.,3.,5.,6.,7.],[2.,4.,8.,9.,1.,3.,5.,6.,7.],[3.,4.,8.,9.,1.,2.,5.,6.,7.],[1.,5., 8.,9.,2.,3.,4.,6.,7.],[2.,5.,8.,9.,1.,3.,4.,6.,7.],[3.,5.,8.,9.,1.,2.,4.,6.,7.],[4.,5 .,8.,9.,1.,2.,3.,6.,7.],[1.,6.,8.,9.,2.,3.,4.,5.,7.],[2.,6.,8.,9.,1.,3.,4.,5.,7.],[3. ,6.,8.,9.,1.,2.,4.,5.,7.],[4.,6.,8.,9.,1.,2.,3.,5.,7.],[5.,6.,8.,9.,1.,2.,3.,4.,7.],[ 1.,7.,8.,9.,2.,3.,4.,5.,6.],[2.,7.,8.,9.,1.,3.,4.,5.,6.],[3.,7.,8.,9.,1.,2.,4.,5.,6.] ,[4.,7.,8.,9.,1.,2.,3.,5.,6.],[5.,7.,8.,9.,1.,2.,3.,4.,6.],[6.,7.,8.,9.,1.,2.,3.,4.,5 .]] L1={{1,2,3,4,5,6,7,8,9},{1,2,3,5,4,6,7,8,9},{1,2,4,5,3,6,7,8,9},{1,3,4,5,2,6,7,8,9},{ 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G. (2025). HP_Prime_MATH: Manual. 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G. (2025). HP_Prime_MATH: Manual. 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,4,5,10,2,6,7,8,9},{2,3,4,5,10,1,6,7,8,9},{1,2,3,6,10,4,5,7,8,9},{1,2,4,6,10,3,5,7,8, 9},{1,3,4,6,10,2,5,7,8,9},{2,3,4,6,10,1,5,7,8,9},{1,2,5,6,10,3,4,7,8,9},{1,3,5,6,10,2 ,4,7,8,9},{2,3,5,6,10,1,4,7,8,9},{1,4,5,6,10,2,3,7,8,9},{2,4,5,6,10,1,3,7,8,9},{3,4,5 ,6,10,1,2,7,8,9},{1,2,3,7,10,4,5,6,8,9},{1,2,4,7,10,3,5,6,8,9},{1,3,4,7,10,2,5,6,8,9} ,{2,3,4,7,10,1,5,6,8,9},{1,2,5,7,10,3,4,6,8,9},{1,3,5,7,10,2,4,6,8,9},{2,3,5,7,10,1,4 ,6,8,9},{1,4,5,7,10,2,3,6,8,9},{2,4,5,7,10,1,3,6,8,9},{3,4,5,7,10,1,2,6,8,9},{1,2,6,7 ,10,3,4,5,8,9},{1,3,6,7,10,2,4,5,8,9},{2,3,6,7,10,1,4,5,8,9},{1,4,6,7,10,2,3,5,8,9},{ 2,4,6,7,10,1,3,5,8,9},{3,4,6,7,10,1,2,5,8,9},{1,5,6,7,10,2,3,4,8,9},{2,5,6,7,10,1,3,4 ,8,9},{3,5,6,7,10,1,2,4,8,9},{4,5,6,7,10,1,2,3,8,9},{1,2,3,8,10,4,5,6,7,9},{1,2,4,8,1 0,3,5,6,7,9},{1,3,4,8,10,2,5,6,7,9},{2,3,4,8,10,1,5,6,7,9},{1,2,5,8,10,3,4,6,7,9},{1, 3,5,8,10,2,4,6,7,9},{2,3,5,8,10,1,4,6,7,9},{1,4,5,8,10,2,3,6,7,9},{2,4,5,8,10,1,3,6,7 ,9},{3,4,5,8,10,1,2,6,7,9},{1,2,6,8,10,3,4,5,7,9},{1,3,6,8,10,2,4,5,7,9},{2,3,6,8,10, 1,4,5,7,9},{1,4,6,8,10,2,3,5,7,9},{2,4,6,8,10,1,3,5,7,9},{3,4,6,8,10,1,2,5,7,9},{1,5, 6,8,10,2,3,4,7,9},{2,5,6,8,10,1,3,4,7,9},{3,5,6,8,10,1,2,4,7,9},{4,5,6,8,10,1,2,3,7,9 },{1,2,7,8,10,3,4,5,6,9},{1,3,7,8,10,2,4,5,6,9},{2,3,7,8,10,1,4,5,6,9},{1,4,7,8,10,2, 3,5,6,9},{2,4,7,8,10,1,3,5,6,9},{3,4,7,8,10,1,2,5,6,9},{1,5,7,8,10,2,3,4,6,9},{2,5,7, 8,10,1,3,4,6,9},{3,5,7,8,10,1,2,4,6,9},{4,5,7,8,10,1,2,3,6,9},{1,6,7,8,10,2,3,4,5,9}, {2,6,7,8,10,1,3,4,5,9},{3,6,7,8,10,1,2,4,5,9},{4,6,7,8,10,1,2,3,5,9},{5,6,7,8,10,1,2, 3,4,9},{1,2,3,9,10,4,5,6,7,8},{1,2,4,9,10,3,5,6,7,8},{1,3,4,9,10,2,5,6,7,8},{2,3,4,9, 10,1,5,6,7,8},{1,2,5,9,10,3,4,6,7,8},{1,3,5,9,10,2,4,6,7,8},{2,3,5,9,10,1,4,6,7,8},{1 ,4,5,9,10,2,3,6,7,8},{2,4,5,9,10,1,3,6,7,8},{3,4,5,9,10,1,2,6,7,8},{1,2,6,9,10,3,4,5, 7,8},{1,3,6,9,10,2,4,5,7,8},{2,3,6,9,10,1,4,5,7,8},{1,4,6,9,10,2,3,5,7,8},{2,4,6,9,10 ,1,3,5,7,8},{3,4,6,9,10,1,2,5,7,8},{1,5,6,9,10,2,3,4,7,8},{2,5,6,9,10,1,3,4,7,8},{3,5 ,6,9,10,1,2,4,7,8},{4,5,6,9,10,1,2,3,7,8},{1,2,7,9,10,3,4,5,6,8},{1,3,7,9,10,2,4,5,6, 8},{2,3,7,9,10,1,4,5,6,8},{1,4,7,9,10,2,3,5,6,8},{2,4,7,9,10,1,3,5,6,8},{3,4,7,9,10,1 ,2,5,6,8},{1,5,7,9,10,2,3,4,6,8},{2,5,7,9,10,1,3,4,6,8},{3,5,7,9,10,1,2,4,6,8},{4,5,7 ,9,10,1,2,3,6,8},{1,6,7,9,10,2,3,4,5,8},{2,6,7,9,10,1,3,4,5,8},{3,6,7,9,10,1,2,4,5,8} ,{4,6,7,9,10,1,2,3,5,8},{5,6,7,9,10,1,2,3,4,8},{1,2,8,9,10,3,4,5,6,7},{1,3,8,9,10,2,4 ,5,6,7},{2,3,8,9,10,1,4,5,6,7},{1,4,8,9,10,2,3,5,6,7},{2,4,8,9,10,1,3,5,6,7},{3,4,8,9 ,10,1,2,5,6,7},{1,5,8,9,10,2,3,4,6,7},{2,5,8,9,10,1,3,4,6,7},{3,5,8,9,10,1,2,4,6,7},{ 4,5,8,9,10,1,2,3,6,7},{1,6,8,9,10,2,3,4,5,7},{2,6,8,9,10,1,3,4,5,7},{3,6,8,9,10,1,2,4 ,5,7},{4,6,8,9,10,1,2,3,5,7},{5,6,8,9,10,1,2,3,4,7},{1,7,8,9,10,2,3,4,5,6},{2,7,8,9,1 Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 83 0,1,3,4,5,6},{3,7,8,9,10,1,2,4,5,6},{4,7,8,9,10,1,2,3,5,6},{5,7,8,9,10,1,2,3,4,6},{6, 7,8,9,10,1,2,3,4,5}} wP12_2_10.dat M1=[[1,2,3,4,5,6,7,8,9,10,11,12],[1,3,2,4,5,6,7,8,9,10,11,12],[2,3,1,4,5,6,7,8,9,10,1 1,12],[1,4,2,3,5,6,7,8,9,10,11,12],[2,4,1,3,5,6,7,8,9,10,11,12],[3,4,1,2,5,6,7,8,9,10 ,11,12],[1,5,2,3,4,6,7,8,9,10,11,12],[2,5,1,3,4,6,7,8,9,10,11,12],[3,5,1,2,4,6,7,8,9, 10,11,12],[4,5,1,2,3,6,7,8,9,10,11,12],[1,6,2,3,4,5,7,8,9,10,11,12],[2,6,1,3,4,5,7,8, 9,10,11,12],[3,6,1,2,4,5,7,8,9,10,11,12],[4,6,1,2,3,5,7,8,9,10,11,12],[5,6,1,2,3,4,7, 8,9,10,11,12],[1,7,2,3,4,5,6,8,9,10,11,12],[2,7,1,3,4,5,6,8,9,10,11,12],[3,7,1,2,4,5, 6,8,9,10,11,12],[4,7,1,2,3,5,6,8,9,10,11,12],[5,7,1,2,3,4,6,8,9,10,11,12],[6,7,1,2,3, 4,5,8,9,10,11,12],[1,8,2,3,4,5,6,7,9,10,11,12],[2,8,1,3,4,5,6,7,9,10,11,12],[3,8,1,2, 4,5,6,7,9,10,11,12],[4,8,1,2,3,5,6,7,9,10,11,12],[5,8,1,2,3,4,6,7,9,10,11,12],[6,8,1, 2,3,4,5,7,9,10,11,12],[7,8,1,2,3,4,5,6,9,10,11,12],[1,9,2,3,4,5,6,7,8,10,11,12],[2,9, 1,3,4,5,6,7,8,10,11,12],[3,9,1,2,4,5,6,7,8,10,11,12],[4,9,1,2,3,5,6,7,8,10,11,12],[5, 9,1,2,3,4,6,7,8,10,11,12],[6,9,1,2,3,4,5,7,8,10,11,12],[7,9,1,2,3,4,5,6,8,10,11,12],[ 8,9,1,2,3,4,5,6,7,10,11,12],[1,10,2,3,4,5,6,7,8,9,11,12],[2,10,1,3,4,5,6,7,8,9,11,12] ,[3,10,1,2,4,5,6,7,8,9,11,12],[4,10,1,2,3,5,6,7,8,9,11,12],[5,10,1,2,3,4,6,7,8,9,11,1 2],[6,10,1,2,3,4,5,7,8,9,11,12],[7,10,1,2,3,4,5,6,8,9,11,12],[8,10,1,2,3,4,5,6,7,9,11 ,12],[9,10,1,2,3,4,5,6,7,8,11,12],[1,11,2,3,4,5,6,7,8,9,10,12],[2,11,1,3,4,5,6,7,8,9, 10,12],[3,11,1,2,4,5,6,7,8,9,10,12],[4,11,1,2,3,5,6,7,8,9,10,12],[5,11,1,2,3,4,6,7,8, 9,10,12],[6,11,1,2,3,4,5,7,8,9,10,12],[7,11,1,2,3,4,5,6,8,9,10,12],[8,11,1,2,3,4,5,6, 7,9,10,12],[9,11,1,2,3,4,5,6,7,8,10,12],[10,11,1,2,3,4,5,6,7,8,9,12],[1,12,2,3,4,5,6, 7,8,9,10,11],[2,12,1,3,4,5,6,7,8,9,10,11],[3,12,1,2,4,5,6,7,8,9,10,11],[4,12,1,2,3,5, 6,7,8,9,10,11],[5,12,1,2,3,4,6,7,8,9,10,11],[6,12,1,2,3,4,5,7,8,9,10,11],[7,12,1,2,3, 4,5,6,8,9,10,11],[8,12,1,2,3,4,5,6,7,9,10,11],[9,12,1,2,3,4,5,6,7,8,10,11],[10,12,1,2 ,3,4,5,6,7,8,9,11],[11,12,1,2,3,4,5,6,7,8,9,10]] L1={{1,2,3,4,5,6,7,8,9,10,11,12},{1,3,2,4,5,6,7,8,9,10,11,12},{2,3,1,4,5,6,7,8,9,10,1 1,12},{1,4,2,3,5,6,7,8,9,10,11,12},{2,4,1,3,5,6,7,8,9,10,11,12},{3,4,1,2,5,6,7,8,9,10 ,11,12},{1,5,2,3,4,6,7,8,9,10,11,12},{2,5,1,3,4,6,7,8,9,10,11,12},{3,5,1,2,4,6,7,8,9, 10,11,12},{4,5,1,2,3,6,7,8,9,10,11,12},{1,6,2,3,4,5,7,8,9,10,11,12},{2,6,1,3,4,5,7,8, 9,10,11,12},{3,6,1,2,4,5,7,8,9,10,11,12},{4,6,1,2,3,5,7,8,9,10,11,12},{5,6,1,2,3,4,7, 8,9,10,11,12},{1,7,2,3,4,5,6,8,9,10,11,12},{2,7,1,3,4,5,6,8,9,10,11,12},{3,7,1,2,4,5, 6,8,9,10,11,12},{4,7,1,2,3,5,6,8,9,10,11,12},{5,7,1,2,3,4,6,8,9,10,11,12},{6,7,1,2,3, 4,5,8,9,10,11,12},{1,8,2,3,4,5,6,7,9,10,11,12},{2,8,1,3,4,5,6,7,9,10,11,12},{3,8,1,2, 4,5,6,7,9,10,11,12},{4,8,1,2,3,5,6,7,9,10,11,12},{5,8,1,2,3,4,6,7,9,10,11,12},{6,8,1, 2,3,4,5,7,9,10,11,12},{7,8,1,2,3,4,5,6,9,10,11,12},{1,9,2,3,4,5,6,7,8,10,11,12},{2,9, 1,3,4,5,6,7,8,10,11,12},{3,9,1,2,4,5,6,7,8,10,11,12},{4,9,1,2,3,5,6,7,8,10,11,12},{5, 9,1,2,3,4,6,7,8,10,11,12},{6,9,1,2,3,4,5,7,8,10,11,12},{7,9,1,2,3,4,5,6,8,10,11,12},{ 8,9,1,2,3,4,5,6,7,10,11,12},{1,10,2,3,4,5,6,7,8,9,11,12},{2,10,1,3,4,5,6,7,8,9,11,12} ,{3,10,1,2,4,5,6,7,8,9,11,12},{4,10,1,2,3,5,6,7,8,9,11,12},{5,10,1,2,3,4,6,7,8,9,11,1 2},{6,10,1,2,3,4,5,7,8,9,11,12},{7,10,1,2,3,4,5,6,8,9,11,12},{8,10,1,2,3,4,5,6,7,9,11 ,12},{9,10,1,2,3,4,5,6,7,8,11,12},{1,11,2,3,4,5,6,7,8,9,10,12},{2,11,1,3,4,5,6,7,8,9, 10,12},{3,11,1,2,4,5,6,7,8,9,10,12},{4,11,1,2,3,5,6,7,8,9,10,12},{5,11,1,2,3,4,6,7,8, 9,10,12},{6,11,1,2,3,4,5,7,8,9,10,12},{7,11,1,2,3,4,5,6,8,9,10,12},{8,11,1,2,3,4,5,6, 7,9,10,12},{9,11,1,2,3,4,5,6,7,8,10,12},{10,11,1,2,3,4,5,6,7,8,9,12},{1,12,2,3,4,5,6, 7,8,9,10,11},{2,12,1,3,4,5,6,7,8,9,10,11},{3,12,1,2,4,5,6,7,8,9,10,11},{4,12,1,2,3,5, 6,7,8,9,10,11},{5,12,1,2,3,4,6,7,8,9,10,11},{6,12,1,2,3,4,5,7,8,9,10,11},{7,12,1,2,3, 4,5,6,8,9,10,11},{8,12,1,2,3,4,5,6,7,9,10,11},{9,12,1,2,3,4,5,6,7,8,10,11},{10,12,1,2 ,3,4,5,6,7,8,9,11},{11,12,1,2,3,4,5,6,7,8,9,10}} wV2_3.dat M1=[[-1,-1,-1],[-1,-1,1],[-1,1,-1],[-1,1,1],[1,-1,-1],[1,-1,1],[1,1,-1],[1,1,1]] L1={{-1,-1,-1},{-1,-1,1},{-1,1,-1},{-1,1,1},{1,-1,-1},{1,-1,1},{1,1,-1},{1,1,1}} wV2_9.dat M1=[[-1,-1,-1,-1,-1,-1,-1,-1,-1],[-1,- 1,-1,-1,-1,-1,-1,-1,1],[-1,-1,-1,-1,- 1,-1,-1,1,-1],[-1,-1,-1,-1,-1,-1,- 1,1,1],[-1,-1,-1,-1,-1,-1,1,-1,-1],[- 1,-1,-1,-1,-1,-1,1,-1,1],[-1,-1,-1,-1,- 1,-1,1,1,-1],[-1,-1,-1,-1,-1,- 1,1,1,1],[-1,-1,-1,-1,-1,1,-1,-1,-1],[- 1,-1,-1,-1,-1,1,-1,-1,1],[-1,-1,-1,-1,- 1,1,-1,1,-1],[-1,-1,-1,-1,-1,1,- 1,1,1],[-1,-1,-1,-1,-1,1,1,-1,-1],[-1,- 1,-1,-1,-1,1,1,-1,1],[-1,-1,-1,-1,- 1,1,1,1,-1],[-1,-1,-1,-1,-1,1,1,1,1],[- 1,-1,-1,-1,1,-1,-1,-1,-1],[-1,-1,-1,- 1,1,-1,-1,-1,1],[-1,-1,-1,-1,1,-1,- 1,1,-1],[-1,-1,-1,-1,1,-1,-1,1,1],[-1,- 1,-1,-1,1,-1,1,-1,-1],[-1,-1,-1,-1,1,- 1,1,-1,1],[-1,-1,-1,-1,1,-1,1,1,-1],[- 1,-1,-1,-1,1,-1,1,1,1],[-1,-1,-1,- 1,1,1,-1,-1,-1],[-1,-1,-1,-1,1,1,-1,- 1,1],[-1,-1,-1,-1,1,1,-1,1,-1],[-1,-1,- 1,-1,1,1,-1,1,1],[-1,-1,-1,-1,1,1,1,- 1,-1],[-1,-1,-1,-1,1,1,1,-1,1],[-1,-1,- 1,-1,1,1,1,1,-1],[-1,-1,-1,- 1,1,1,1,1,1],[-1,-1,-1,1,-1,-1,-1,-1,- 1],[-1,-1,-1,1,-1,-1,-1,-1,1],[-1,-1,- 1,1,-1,-1,-1,1,-1],[-1,-1,-1,1,-1,-1,- 1,1,1],[-1,-1,-1,1,-1,-1,1,-1,-1],[-1,- 1,-1,1,-1,-1,1,-1,1],[-1,-1,-1,1,-1,- 1,1,1,-1],[-1,-1,-1,1,-1,-1,1,1,1],[- 1,-1,-1,1,-1,1,-1,-1,-1],[-1,-1,-1,1,- 1,1,-1,-1,1],[-1,-1,-1,1,-1,1,-1,1,- 1],[-1,-1,-1,1,-1,1,-1,1,1],[-1,-1,- 1,1,-1,1,1,-1,-1],[-1,-1,-1,1,-1,1,1,- 1,1],[-1,-1,-1,1,-1,1,1,1,-1],[-1,-1,- Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 84 1,1,-1,1,1,1,1],[-1,-1,-1,1,1,-1,-1,- 1,-1],[-1,-1,-1,1,1,-1,-1,-1,1],[-1,- 1,-1,1,1,-1,-1,1,-1],[-1,-1,-1,1,1,-1,- 1,1,1],[-1,-1,-1,1,1,-1,1,-1,-1],[-1,- 1,-1,1,1,-1,1,-1,1],[-1,-1,-1,1,1,- 1,1,1,-1],[-1,-1,-1,1,1,-1,1,1,1],[-1,- 1,-1,1,1,1,-1,-1,-1],[-1,-1,-1,1,1,1,- 1,-1,1],[-1,-1,-1,1,1,1,-1,1,-1],[-1,- 1,-1,1,1,1,-1,1,1],[-1,-1,-1,1,1,1,1,- 1,-1],[-1,-1,-1,1,1,1,1,-1,1],[-1,-1,- 1,1,1,1,1,1,-1],[-1,-1,- 1,1,1,1,1,1,1],[-1,-1,1,-1,-1,-1,-1,- 1,-1],[-1,-1,1,-1,-1,-1,-1,-1,1],[-1,- 1,1,-1,-1,-1,-1,1,-1],[-1,-1,1,-1,-1,- 1,-1,1,1],[-1,-1,1,-1,-1,-1,1,-1,-1],[- 1,-1,1,-1,-1,-1,1,-1,1],[-1,-1,1,-1,- 1,-1,1,1,-1],[-1,-1,1,-1,-1,- 1,1,1,1],[-1,-1,1,-1,-1,1,-1,-1,-1],[- 1,-1,1,-1,-1,1,-1,-1,1],[-1,-1,1,-1,- 1,1,-1,1,-1],[-1,-1,1,-1,-1,1,- 1,1,1],[-1,-1,1,-1,-1,1,1,-1,-1],[-1,- 1,1,-1,-1,1,1,-1,1],[-1,-1,1,-1,- 1,1,1,1,-1],[-1,-1,1,-1,-1,1,1,1,1],[- 1,-1,1,-1,1,-1,-1,-1,-1],[-1,-1,1,- 1,1,-1,-1,-1,1],[-1,-1,1,-1,1,-1,-1,1,- 1],[-1,-1,1,-1,1,-1,-1,1,1],[-1,-1,1,- 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1,1,1,-1,1],[-1,1,1,1,-1,1,1,1,-1],[- 1,1,1,1,-1,1,1,1,1],[-1,1,1,1,1,-1,-1,- 1,-1],[-1,1,1,1,1,-1,-1,-1,1],[- 1,1,1,1,1,-1,-1,1,-1],[-1,1,1,1,1,-1,- 1,1,1],[-1,1,1,1,1,-1,1,-1,-1],[- 1,1,1,1,1,-1,1,-1,1],[-1,1,1,1,1,- 1,1,1,-1],[-1,1,1,1,1,-1,1,1,1],[- 1,1,1,1,1,1,-1,-1,-1],[-1,1,1,1,1,1,- 1,-1,1],[-1,1,1,1,1,1,-1,1,-1],[- 1,1,1,1,1,1,-1,1,1],[-1,1,1,1,1,1,1,- 1,-1],[-1,1,1,1,1,1,1,-1,1],[- 1,1,1,1,1,1,1,1,-1],[- 1,1,1,1,1,1,1,1,1],[1,-1,-1,-1,-1,-1,- 1,-1,-1],[1,-1,-1,-1,-1,-1,-1,- 1,1],[1,-1,-1,-1,-1,-1,-1,1,-1],[1,-1,- 1,-1,-1,-1,-1,1,1],[1,-1,-1,-1,-1,- 1,1,-1,-1],[1,-1,-1,-1,-1,-1,1,- 1,1],[1,-1,-1,-1,-1,-1,1,1,-1],[1,-1,- 1,-1,-1,-1,1,1,1],[1,-1,-1,-1,-1,1,-1,- 1,-1],[1,-1,-1,-1,-1,1,-1,-1,1],[1,-1,- 1,-1,-1,1,-1,1,-1],[1,-1,-1,-1,-1,1,- 1,1,1],[1,-1,-1,-1,-1,1,1,-1,-1],[1,- 1,-1,-1,-1,1,1,-1,1],[1,-1,-1,-1,- 1,1,1,1,-1],[1,-1,-1,-1,- 1,1,1,1,1],[1,-1,-1,-1,1,-1,-1,-1,- 1],[1,-1,-1,-1,1,-1,-1,-1,1],[1,-1,-1,- Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 85 1,1,-1,-1,1,-1],[1,-1,-1,-1,1,-1,- 1,1,1],[1,-1,-1,-1,1,-1,1,-1,-1],[1,- 1,-1,-1,1,-1,1,-1,1],[1,-1,-1,-1,1,- 1,1,1,-1],[1,-1,-1,-1,1,-1,1,1,1],[1,- 1,-1,-1,1,1,-1,-1,-1],[1,-1,-1,-1,1,1,- 1,-1,1],[1,-1,-1,-1,1,1,-1,1,-1],[1,- 1,-1,-1,1,1,-1,1,1],[1,-1,-1,-1,1,1,1,- 1,-1],[1,-1,-1,-1,1,1,1,-1,1],[1,-1,- 1,-1,1,1,1,1,-1],[1,-1,-1,- 1,1,1,1,1,1],[1,-1,-1,1,-1,-1,-1,-1,- 1],[1,-1,-1,1,-1,-1,-1,-1,1],[1,-1,- 1,1,-1,-1,-1,1,-1],[1,-1,-1,1,-1,-1,- 1,1,1],[1,-1,-1,1,-1,-1,1,-1,-1],[1,- 1,-1,1,-1,-1,1,-1,1],[1,-1,-1,1,-1,- 1,1,1,-1],[1,-1,-1,1,-1,-1,1,1,1],[1,- 1,-1,1,-1,1,-1,-1,-1],[1,-1,-1,1,-1,1,- 1,-1,1],[1,-1,-1,1,-1,1,-1,1,-1],[1,- 1,-1,1,-1,1,-1,1,1],[1,-1,-1,1,-1,1,1,- 1,-1],[1,-1,-1,1,-1,1,1,-1,1],[1,-1,- 1,1,-1,1,1,1,-1],[1,-1,-1,1,- 1,1,1,1,1],[1,-1,-1,1,1,-1,-1,-1,- 1],[1,-1,-1,1,1,-1,-1,-1,1],[1,-1,- 1,1,1,-1,-1,1,-1],[1,-1,-1,1,1,-1,- 1,1,1],[1,-1,-1,1,1,-1,1,-1,-1],[1,-1,- 1,1,1,-1,1,-1,1],[1,-1,-1,1,1,-1,1,1,- 1],[1,-1,-1,1,1,-1,1,1,1],[1,-1,- 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1,1,1,1],[1,1,1,-1,1,1,-1,-1,- 1],[1,1,1,-1,1,1,-1,-1,1],[1,1,1,- 1,1,1,-1,1,-1],[1,1,1,-1,1,1,- 1,1,1],[1,1,1,-1,1,1,1,-1,-1],[1,1,1,- 1,1,1,1,-1,1],[1,1,1,-1,1,1,1,1,- 1],[1,1,1,-1,1,1,1,1,1],[1,1,1,1,-1,- 1,-1,-1,-1],[1,1,1,1,-1,-1,-1,- 1,1],[1,1,1,1,-1,-1,-1,1,-1],[1,1,1,1,- 1,-1,-1,1,1],[1,1,1,1,-1,-1,1,-1,- 1],[1,1,1,1,-1,-1,1,-1,1],[1,1,1,1,-1,- 1,1,1,-1],[1,1,1,1,-1,- 1,1,1,1],[1,1,1,1,-1,1,-1,-1,- 1],[1,1,1,1,-1,1,-1,-1,1],[1,1,1,1,- 1,1,-1,1,-1],[1,1,1,1,-1,1,- 1,1,1],[1,1,1,1,-1,1,1,-1,- 1],[1,1,1,1,-1,1,1,-1,1],[1,1,1,1,- 1,1,1,1,-1],[1,1,1,1,- 1,1,1,1,1],[1,1,1,1,1,-1,-1,-1,- 1],[1,1,1,1,1,-1,-1,-1,1],[1,1,1,1,1,- 1,-1,1,-1],[1,1,1,1,1,-1,- Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 86 1,1,1],[1,1,1,1,1,-1,1,-1,- 1],[1,1,1,1,1,-1,1,-1,1],[1,1,1,1,1,- 1,1,1,-1],[1,1,1,1,1,- 1,1,1,1],[1,1,1,1,1,1,-1,-1,- 1],[1,1,1,1,1,1,-1,-1,1],[1,1,1,1,1,1,- 1,1,-1],[1,1,1,1,1,1,- 1,1,1],[1,1,1,1,1,1,1,-1,- 1],[1,1,1,1,1,1,1,- 1,1],[1,1,1,1,1,1,1,1,- 1],[1,1,1,1,1,1,1,1,1]] L1={{-1,-1,-1,-1,-1,-1,-1,-1,-1},{-1,- 1,-1,-1,-1,-1,-1,-1,1},{-1,-1,-1,-1,- 1,-1,-1,1,-1},{-1,-1,-1,-1,-1,-1,- 1,1,1},{-1,-1,-1,-1,-1,-1,1,-1,-1},{- 1,-1,-1,-1,-1,-1,1,-1,1},{-1,-1,-1,-1,- 1,-1,1,1,-1},{-1,-1,-1,-1,-1,- 1,1,1,1},{-1,-1,-1,-1,-1,1,-1,-1,-1},{- 1,-1,-1,-1,-1,1,-1,-1,1},{-1,-1,-1,-1,- 1,1,-1,1,-1},{-1,-1,-1,-1,-1,1,- 1,1,1},{-1,-1,-1,-1,-1,1,1,-1,-1},{-1,- 1,-1,-1,-1,1,1,-1,1},{-1,-1,-1,-1,- 1,1,1,1,-1},{-1,-1,-1,-1,-1,1,1,1,1},{- 1,-1,-1,-1,1,-1,-1,-1,-1},{-1,-1,-1,- 1,1,-1,-1,-1,1},{-1,-1,-1,-1,1,-1,- 1,1,-1},{-1,-1,-1,-1,1,-1,-1,1,1},{-1,- 1,-1,-1,1,-1,1,-1,-1},{-1,-1,-1,-1,1,- 1,1,-1,1},{-1,-1,-1,-1,1,-1,1,1,-1},{- 1,-1,-1,-1,1,-1,1,1,1},{-1,-1,-1,- 1,1,1,-1,-1,-1},{-1,-1,-1,-1,1,1,-1,- 1,1},{-1,-1,-1,-1,1,1,-1,1,-1},{-1,-1,- 1,-1,1,1,-1,1,1},{-1,-1,-1,-1,1,1,1,- 1,-1},{-1,-1,-1,-1,1,1,1,-1,1},{-1,-1,- 1,-1,1,1,1,1,-1},{-1,-1,-1,- 1,1,1,1,1,1},{-1,-1,-1,1,-1,-1,-1,-1,- 1},{-1,-1,-1,1,-1,-1,-1,-1,1},{-1,-1,- 1,1,-1,-1,-1,1,-1},{-1,-1,-1,1,-1,-1,- 1,1,1},{-1,-1,-1,1,-1,-1,1,-1,-1},{-1,- 1,-1,1,-1,-1,1,-1,1},{-1,-1,-1,1,-1,- 1,1,1,-1},{-1,-1,-1,1,-1,-1,1,1,1},{- 1,-1,-1,1,-1,1,-1,-1,-1},{-1,-1,-1,1,- 1,1,-1,-1,1},{-1,-1,-1,1,-1,1,-1,1,- 1},{-1,-1,-1,1,-1,1,-1,1,1},{-1,-1,- 1,1,-1,1,1,-1,-1},{-1,-1,-1,1,-1,1,1,- 1,1},{-1,-1,-1,1,-1,1,1,1,-1},{-1,-1,- 1,1,-1,1,1,1,1},{-1,-1,-1,1,1,-1,-1,- 1,-1},{-1,-1,-1,1,1,-1,-1,-1,1},{-1,- 1,-1,1,1,-1,-1,1,-1},{-1,-1,-1,1,1,-1,- 1,1,1},{-1,-1,-1,1,1,-1,1,-1,-1},{-1,- 1,-1,1,1,-1,1,-1,1},{-1,-1,-1,1,1,- 1,1,1,-1},{-1,-1,-1,1,1,-1,1,1,1},{-1,- 1,-1,1,1,1,-1,-1,-1},{-1,-1,-1,1,1,1,- 1,-1,1},{-1,-1,-1,1,1,1,-1,1,-1},{-1,- 1,-1,1,1,1,-1,1,1},{-1,-1,-1,1,1,1,1,- 1,-1},{-1,-1,-1,1,1,1,1,-1,1},{-1,-1,- 1,1,1,1,1,1,-1},{-1,-1,- 1,1,1,1,1,1,1},{-1,-1,1,-1,-1,-1,-1,- 1,-1},{-1,-1,1,-1,-1,-1,-1,-1,1},{-1,- 1,1,-1,-1,-1,-1,1,-1},{-1,-1,1,-1,-1,- 1,-1,1,1},{-1,-1,1,-1,-1,-1,1,-1,-1},{- 1,-1,1,-1,-1,-1,1,-1,1},{-1,-1,1,-1,- 1,-1,1,1,-1},{-1,-1,1,-1,-1,- 1,1,1,1},{-1,-1,1,-1,-1,1,-1,-1,-1},{- 1,-1,1,-1,-1,1,-1,-1,1},{-1,-1,1,-1,- 1,1,-1,1,-1},{-1,-1,1,-1,-1,1,- 1,1,1},{-1,-1,1,-1,-1,1,1,-1,-1},{-1,- 1,1,-1,-1,1,1,-1,1},{-1,-1,1,-1,- 1,1,1,1,-1},{-1,-1,1,-1,-1,1,1,1,1},{- 1,-1,1,-1,1,-1,-1,-1,-1},{-1,-1,1,- 1,1,-1,-1,-1,1},{-1,-1,1,-1,1,-1,-1,1,- 1},{-1,-1,1,-1,1,-1,-1,1,1},{-1,-1,1,- 1,1,-1,1,-1,-1},{-1,-1,1,-1,1,-1,1,- 1,1},{-1,-1,1,-1,1,-1,1,1,-1},{-1,- 1,1,-1,1,-1,1,1,1},{-1,-1,1,-1,1,1,-1,- 1,-1},{-1,-1,1,-1,1,1,-1,-1,1},{-1,- 1,1,-1,1,1,-1,1,-1},{-1,-1,1,-1,1,1,- 1,1,1},{-1,-1,1,-1,1,1,1,-1,-1},{-1,- 1,1,-1,1,1,1,-1,1},{-1,-1,1,- 1,1,1,1,1,-1},{-1,-1,1,-1,1,1,1,1,1},{- 1,-1,1,1,-1,-1,-1,-1,-1},{-1,-1,1,1,- 1,-1,-1,-1,1},{-1,-1,1,1,-1,-1,-1,1,- 1},{-1,-1,1,1,-1,-1,-1,1,1},{-1,- 1,1,1,-1,-1,1,-1,-1},{-1,-1,1,1,-1,- 1,1,-1,1},{-1,-1,1,1,-1,-1,1,1,-1},{- 1,-1,1,1,-1,-1,1,1,1},{-1,-1,1,1,-1,1,- 1,-1,-1},{-1,-1,1,1,-1,1,-1,-1,1},{-1,- 1,1,1,-1,1,-1,1,-1},{-1,-1,1,1,-1,1,- 1,1,1},{-1,-1,1,1,-1,1,1,-1,-1},{-1,- 1,1,1,-1,1,1,-1,1},{-1,-1,1,1,- 1,1,1,1,-1},{-1,-1,1,1,-1,1,1,1,1},{- 1,-1,1,1,1,-1,-1,-1,-1},{-1,-1,1,1,1,- 1,-1,-1,1},{-1,-1,1,1,1,-1,-1,1,-1},{- 1,-1,1,1,1,-1,-1,1,1},{-1,-1,1,1,1,- 1,1,-1,-1},{-1,-1,1,1,1,-1,1,-1,1},{- 1,-1,1,1,1,-1,1,1,-1},{-1,-1,1,1,1,- 1,1,1,1},{-1,-1,1,1,1,1,-1,-1,-1},{-1,- 1,1,1,1,1,-1,-1,1},{-1,-1,1,1,1,1,- 1,1,-1},{-1,-1,1,1,1,1,-1,1,1},{-1,- 1,1,1,1,1,1,-1,-1},{-1,-1,1,1,1,1,1,- 1,1},{-1,-1,1,1,1,1,1,1,-1},{-1,- 1,1,1,1,1,1,1,1},{-1,1,-1,-1,-1,-1,-1,- 1,-1},{-1,1,-1,-1,-1,-1,-1,-1,1},{- 1,1,-1,-1,-1,-1,-1,1,-1},{-1,1,-1,-1,- 1,-1,-1,1,1},{-1,1,-1,-1,-1,-1,1,-1,- 1},{-1,1,-1,-1,-1,-1,1,-1,1},{-1,1,-1,- 1,-1,-1,1,1,-1},{-1,1,-1,-1,-1,- 1,1,1,1},{-1,1,-1,-1,-1,1,-1,-1,-1},{- 1,1,-1,-1,-1,1,-1,-1,1},{-1,1,-1,-1,- 1,1,-1,1,-1},{-1,1,-1,-1,-1,1,- 1,1,1},{-1,1,-1,-1,-1,1,1,-1,-1},{- 1,1,-1,-1,-1,1,1,-1,1},{-1,1,-1,-1,- 1,1,1,1,-1},{-1,1,-1,-1,-1,1,1,1,1},{- 1,1,-1,-1,1,-1,-1,-1,-1},{-1,1,-1,- 1,1,-1,-1,-1,1},{-1,1,-1,-1,1,-1,-1,1,- 1},{-1,1,-1,-1,1,-1,-1,1,1},{-1,1,-1,- 1,1,-1,1,-1,-1},{-1,1,-1,-1,1,-1,1,- 1,1},{-1,1,-1,-1,1,-1,1,1,-1},{-1,1,- 1,-1,1,-1,1,1,1},{-1,1,-1,-1,1,1,-1,- 1,-1},{-1,1,-1,-1,1,1,-1,-1,1},{-1,1,- 1,-1,1,1,-1,1,-1},{-1,1,-1,-1,1,1,- 1,1,1},{-1,1,-1,-1,1,1,1,-1,-1},{-1,1,- 1,-1,1,1,1,-1,1},{-1,1,-1,-1,1,1,1,1,- 1},{-1,1,-1,-1,1,1,1,1,1},{-1,1,-1,1,- 1,-1,-1,-1,-1},{-1,1,-1,1,-1,-1,-1,- 1,1},{-1,1,-1,1,-1,-1,-1,1,-1},{-1,1,- 1,1,-1,-1,-1,1,1},{-1,1,-1,1,-1,-1,1,- 1,-1},{-1,1,-1,1,-1,-1,1,-1,1},{-1,1,- 1,1,-1,-1,1,1,-1},{-1,1,-1,1,-1,- 1,1,1,1},{-1,1,-1,1,-1,1,-1,-1,-1},{- 1,1,-1,1,-1,1,-1,-1,1},{-1,1,-1,1,- 1,1,-1,1,-1},{-1,1,-1,1,-1,1,-1,1,1},{- 1,1,-1,1,-1,1,1,-1,-1},{-1,1,-1,1,- 1,1,1,-1,1},{-1,1,-1,1,-1,1,1,1,-1},{- 1,1,-1,1,-1,1,1,1,1},{-1,1,-1,1,1,-1,- 1,-1,-1},{-1,1,-1,1,1,-1,-1,-1,1},{- 1,1,-1,1,1,-1,-1,1,-1},{-1,1,-1,1,1,- 1,-1,1,1},{-1,1,-1,1,1,-1,1,-1,-1},{- 1,1,-1,1,1,-1,1,-1,1},{-1,1,-1,1,1,- 1,1,1,-1},{-1,1,-1,1,1,-1,1,1,1},{- 1,1,-1,1,1,1,-1,-1,-1},{-1,1,-1,1,1,1,- 1,-1,1},{-1,1,-1,1,1,1,-1,1,-1},{-1,1,- 1,1,1,1,-1,1,1},{-1,1,-1,1,1,1,1,-1,- 1},{-1,1,-1,1,1,1,1,-1,1},{-1,1,- 1,1,1,1,1,1,-1},{-1,1,- 1,1,1,1,1,1,1},{-1,1,1,-1,-1,-1,-1,-1,- 1},{-1,1,1,-1,-1,-1,-1,-1,1},{-1,1,1,- 1,-1,-1,-1,1,-1},{-1,1,1,-1,-1,-1,- 1,1,1},{-1,1,1,-1,-1,-1,1,-1,-1},{- 1,1,1,-1,-1,-1,1,-1,1},{-1,1,1,-1,-1,- 1,1,1,-1},{-1,1,1,-1,-1,-1,1,1,1},{- 1,1,1,-1,-1,1,-1,-1,-1},{-1,1,1,-1,- 1,1,-1,-1,1},{-1,1,1,-1,-1,1,-1,1,- 1},{-1,1,1,-1,-1,1,-1,1,1},{-1,1,1,-1,- 1,1,1,-1,-1},{-1,1,1,-1,-1,1,1,-1,1},{- 1,1,1,-1,-1,1,1,1,-1},{-1,1,1,-1,- 1,1,1,1,1},{-1,1,1,-1,1,-1,-1,-1,-1},{- Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 93 1,1,1,1],[1,1,1,-1,1,1,1,-1,-1,- 1],[1,1,1,-1,1,1,1,-1,-1,1],[1,1,1,- 1,1,1,1,-1,1,-1],[1,1,1,-1,1,1,1,- 1,1,1],[1,1,1,-1,1,1,1,1,-1,- 1],[1,1,1,-1,1,1,1,1,-1,1],[1,1,1,- 1,1,1,1,1,1,-1],[1,1,1,- 1,1,1,1,1,1,1],[1,1,1,1,-1,-1,-1,-1,- 1,-1],[1,1,1,1,-1,-1,-1,-1,- 1,1],[1,1,1,1,-1,-1,-1,-1,1,- 1],[1,1,1,1,-1,-1,-1,-1,1,1],[1,1,1,1,- 1,-1,-1,1,-1,-1],[1,1,1,1,-1,-1,-1,1,- 1,1],[1,1,1,1,-1,-1,-1,1,1,- 1],[1,1,1,1,-1,-1,-1,1,1,1],[1,1,1,1,- 1,-1,1,-1,-1,-1],[1,1,1,1,-1,-1,1,-1,- 1,1],[1,1,1,1,-1,-1,1,-1,1,- 1],[1,1,1,1,-1,-1,1,-1,1,1],[1,1,1,1,- 1,-1,1,1,-1,-1],[1,1,1,1,-1,-1,1,1,- 1,1],[1,1,1,1,-1,-1,1,1,1,- 1],[1,1,1,1,-1,-1,1,1,1,1],[1,1,1,1,- 1,1,-1,-1,-1,-1],[1,1,1,1,-1,1,-1,-1,- 1,1],[1,1,1,1,-1,1,-1,-1,1,- 1],[1,1,1,1,-1,1,-1,-1,1,1],[1,1,1,1,- 1,1,-1,1,-1,-1],[1,1,1,1,-1,1,-1,1,- 1,1],[1,1,1,1,-1,1,-1,1,1,- 1],[1,1,1,1,-1,1,-1,1,1,1],[1,1,1,1,- 1,1,1,-1,-1,-1],[1,1,1,1,-1,1,1,-1,- 1,1],[1,1,1,1,-1,1,1,-1,1,- 1],[1,1,1,1,-1,1,1,-1,1,1],[1,1,1,1,- 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G. (2025). HP_Prime_MATH: Manual. 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G. (2025). HP_Prime_MATH: Manual. OL60452436M 95 1,-1,-1,1,-1,-1},{-1,1,-1,1,-1,-1,- 1,1,-1,1},{-1,1,-1,1,-1,-1,-1,1,1,- 1},{-1,1,-1,1,-1,-1,-1,1,1,1},{-1,1,- 1,1,-1,-1,1,-1,-1,-1},{-1,1,-1,1,-1,- 1,1,-1,-1,1},{-1,1,-1,1,-1,-1,1,-1,1,- 1},{-1,1,-1,1,-1,-1,1,-1,1,1},{-1,1,- 1,1,-1,-1,1,1,-1,-1},{-1,1,-1,1,-1,- 1,1,1,-1,1},{-1,1,-1,1,-1,-1,1,1,1,- 1},{-1,1,-1,1,-1,-1,1,1,1,1},{-1,1,- 1,1,-1,1,-1,-1,-1,-1},{-1,1,-1,1,-1,1,- 1,-1,-1,1},{-1,1,-1,1,-1,1,-1,-1,1,- 1},{-1,1,-1,1,-1,1,-1,-1,1,1},{-1,1,- 1,1,-1,1,-1,1,-1,-1},{-1,1,-1,1,-1,1,- 1,1,-1,1},{-1,1,-1,1,-1,1,-1,1,1,-1},{- 1,1,-1,1,-1,1,-1,1,1,1},{-1,1,-1,1,- 1,1,1,-1,-1,-1},{-1,1,-1,1,-1,1,1,-1,- 1,1},{-1,1,-1,1,-1,1,1,-1,1,-1},{-1,1,- 1,1,-1,1,1,-1,1,1},{-1,1,-1,1,- 1,1,1,1,-1,-1},{-1,1,-1,1,-1,1,1,1,- 1,1},{-1,1,-1,1,-1,1,1,1,1,-1},{-1,1,- 1,1,-1,1,1,1,1,1},{-1,1,-1,1,1,-1,-1,- 1,-1,-1},{-1,1,-1,1,1,-1,-1,-1,-1,1},{- 1,1,-1,1,1,-1,-1,-1,1,-1},{-1,1,- 1,1,1,-1,-1,-1,1,1},{-1,1,-1,1,1,-1,- 1,1,-1,-1},{-1,1,-1,1,1,-1,-1,1,- 1,1},{-1,1,-1,1,1,-1,-1,1,1,-1},{-1,1,- 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1,1,1,-1},{-1,1,1,1,1,1,-1,1,1,1},{- 1,1,1,1,1,1,1,-1,-1,-1},{- 1,1,1,1,1,1,1,-1,-1,1},{- 1,1,1,1,1,1,1,-1,1,-1},{- 1,1,1,1,1,1,1,-1,1,1},{- 1,1,1,1,1,1,1,1,-1,-1},{- 1,1,1,1,1,1,1,1,-1,1},{- 1,1,1,1,1,1,1,1,1,-1},{- 1,1,1,1,1,1,1,1,1,1},{1,-1,-1,-1,-1,- 1,-1,-1,-1,-1},{1,-1,-1,-1,-1,-1,-1,- 1,-1,1},{1,-1,-1,-1,-1,-1,-1,-1,1,- 1},{1,-1,-1,-1,-1,-1,-1,-1,1,1},{1,-1,- 1,-1,-1,-1,-1,1,-1,-1},{1,-1,-1,-1,-1,- 1,-1,1,-1,1},{1,-1,-1,-1,-1,-1,-1,1,1,- 1},{1,-1,-1,-1,-1,-1,-1,1,1,1},{1,-1,- 1,-1,-1,-1,1,-1,-1,-1},{1,-1,-1,-1,-1,- 1,1,-1,-1,1},{1,-1,-1,-1,-1,-1,1,-1,1,- 1},{1,-1,-1,-1,-1,-1,1,-1,1,1},{1,-1,- 1,-1,-1,-1,1,1,-1,-1},{1,-1,-1,-1,-1,- 1,1,1,-1,1},{1,-1,-1,-1,-1,-1,1,1,1,- 1},{1,-1,-1,-1,-1,-1,1,1,1,1},{1,-1,- 1,-1,-1,1,-1,-1,-1,-1},{1,-1,-1,-1,- 1,1,-1,-1,-1,1},{1,-1,-1,-1,-1,1,-1,- Schrausser, D. G. (2025). HP_Prime_MATH: Manual. OL60452436M 96 1,1,-1},{1,-1,-1,-1,-1,1,-1,- 1,1,1},{1,-1,-1,-1,-1,1,-1,1,-1,- 1},{1,-1,-1,-1,-1,1,-1,1,-1,1},{1,-1,- 1,-1,-1,1,-1,1,1,-1},{1,-1,-1,-1,-1,1,- 1,1,1,1},{1,-1,-1,-1,-1,1,1,-1,-1,- 1},{1,-1,-1,-1,-1,1,1,-1,-1,1},{1,-1,- 1,-1,-1,1,1,-1,1,-1},{1,-1,-1,-1,- 1,1,1,-1,1,1},{1,-1,-1,-1,-1,1,1,1,-1,- 1},{1,-1,-1,-1,-1,1,1,1,-1,1},{1,-1,- 1,-1,-1,1,1,1,1,-1},{1,-1,-1,-1,- 1,1,1,1,1,1},{1,-1,-1,-1,1,-1,-1,-1,- 1,-1},{1,-1,-1,-1,1,-1,-1,-1,-1,1},{1,- 1,-1,-1,1,-1,-1,-1,1,-1},{1,-1,-1,- 1,1,-1,-1,-1,1,1},{1,-1,-1,-1,1,-1,- 1,1,-1,-1},{1,-1,-1,-1,1,-1,-1,1,- 1,1},{1,-1,-1,-1,1,-1,-1,1,1,-1},{1,- 1,-1,-1,1,-1,-1,1,1,1},{1,-1,-1,-1,1,- 1,1,-1,-1,-1},{1,-1,-1,-1,1,-1,1,-1,- 1,1},{1,-1,-1,-1,1,-1,1,-1,1,-1},{1,- 1,-1,-1,1,-1,1,-1,1,1},{1,-1,-1,-1,1,- 1,1,1,-1,-1},{1,-1,-1,-1,1,-1,1,1,- 1,1},{1,-1,-1,-1,1,-1,1,1,1,-1},{1,-1,- 1,-1,1,-1,1,1,1,1},{1,-1,-1,-1,1,1,-1,- 1,-1,-1},{1,-1,-1,-1,1,1,-1,-1,- 1,1},{1,-1,-1,-1,1,1,-1,-1,1,-1},{1,- 1,-1,-1,1,1,-1,-1,1,1},{1,-1,-1,- 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1,1,1},{1,-1,-1,1,1,1,1,1,-1,-1},{1,- 1,-1,1,1,1,1,1,-1,1},{1,-1,- 1,1,1,1,1,1,1,-1},{1,-1,- 1,1,1,1,1,1,1,1},{1,-1,1,-1,-1,-1,-1,- 1,-1,-1},{1,-1,1,-1,-1,-1,-1,-1,- 1,1},{1,-1,1,-1,-1,-1,-1,-1,1,-1},{1,- 1,1,-1,-1,-1,-1,-1,1,1},{1,-1,1,-1,-1,- 1,-1,1,-1,-1},{1,-1,1,-1,-1,-1,-1,1,- 1,1},{1,-1,1,-1,-1,-1,-1,1,1,-1},{1,- 1,1,-1,-1,-1,-1,1,1,1},{1,-1,1,-1,-1,- 1,1,-1,-1,-1},{1,-1,1,-1,-1,-1,1,-1,- 1,1},{1,-1,1,-1,-1,-1,1,-1,1,-1},{1,- 1,1,-1,-1,-1,1,-1,1,1},{1,-1,1,-1,-1,- 1,1,1,-1,-1},{1,-1,1,-1,-1,-1,1,1,- 1,1},{1,-1,1,-1,-1,-1,1,1,1,-1},{1,- 1,1,-1,-1,-1,1,1,1,1},{1,-1,1,-1,-1,1,- 1,-1,-1,-1},{1,-1,1,-1,-1,1,-1,-1,- 1,1},{1,-1,1,-1,-1,1,-1,-1,1,-1},{1,- 1,1,-1,-1,1,-1,-1,1,1},{1,-1,1,-1,- 1,1,-1,1,-1,-1},{1,-1,1,-1,-1,1,-1,1,- 1,1},{1,-1,1,-1,-1,1,-1,1,1,-1},{1,- 1,1,-1,-1,1,-1,1,1,1},{1,-1,1,-1,- 1,1,1,-1,-1,-1},{1,-1,1,-1,-1,1,1,-1,- 1,1},{1,-1,1,-1,-1,1,1,-1,1,-1},{1,- 1,1,-1,-1,1,1,-1,1,1},{1,-1,1,-1,- 1,1,1,1,-1,-1},{1,-1,1,-1,-1,1,1,1,- 1,1},{1,-1,1,-1,-1,1,1,1,1,-1},{1,- 1,1,-1,-1,1,1,1,1,1},{1,-1,1,-1,1,-1,- 1,-1,-1,-1},{1,-1,1,-1,1,-1,-1,-1,- 1,1},{1,-1,1,-1,1,-1,-1,-1,1,-1},{1,- 1,1,-1,1,-1,-1,-1,1,1},{1,-1,1,-1,1,- 1,-1,1,-1,-1},{1,-1,1,-1,1,-1,-1,1,- 1,1},{1,-1,1,-1,1,-1,-1,1,1,-1},{1,- 1,1,-1,1,-1,-1,1,1,1},{1,-1,1,-1,1,- 1,1,-1,-1,-1},{1,-1,1,-1,1,-1,1,-1,- 1,1},{1,-1,1,-1,1,-1,1,-1,1,-1},{1,- 1,1,-1,1,-1,1,-1,1,1},{1,-1,1,-1,1,- 1,1,1,-1,-1},{1,-1,1,-1,1,-1,1,1,- 1,1},{1,-1,1,-1,1,-1,1,1,1,-1},{1,- 1,1,-1,1,-1,1,1,1,1},{1,-1,1,-1,1,1,- 1,-1,-1,-1},{1,-1,1,-1,1,1,-1,-1,- 1,1},{1,-1,1,-1,1,1,-1,-1,1,-1},{1,- 1,1,-1,1,1,-1,-1,1,1},{1,-1,1,-1,1,1,- 1,1,-1,-1},{1,-1,1,-1,1,1,-1,1,- 1,1},{1,-1,1,-1,1,1,-1,1,1,-1},{1,- 1,1,-1,1,1,-1,1,1,1},{1,-1,1,-1,1,1,1,- 1,-1,-1},{1,-1,1,-1,1,1,1,-1,-1,1},{1,- 1,1,-1,1,1,1,-1,1,-1},{1,-1,1,- 1,1,1,1,-1,1,1},{1,-1,1,-1,1,1,1,1,-1,- 1},{1,-1,1,-1,1,1,1,1,-1,1},{1,-1,1,- 1,1,1,1,1,1,-1},{1,-1,1,- 1,1,1,1,1,1,1},{1,-1,1,1,-1,-1,-1,-1,- 1,-1},{1,-1,1,1,-1,-1,-1,-1,-1,1},{1,- 1,1,1,-1,-1,-1,-1,1,-1},{1,-1,1,1,-1,- 1,-1,-1,1,1},{1,-1,1,1,-1,-1,-1,1,-1,- 1},{1,-1,1,1,-1,-1,-1,1,-1,1},{1,- 1,1,1,-1,-1,-1,1,1,-1},{1,-1,1,1,-1,- 1,-1,1,1,1},{1,-1,1,1,-1,-1,1,-1,-1,- 1},{1,-1,1,1,-1,-1,1,-1,-1,1},{1,- 1,1,1,-1,-1,1,-1,1,-1},{1,-1,1,1,-1,- 1,1,-1,1,1},{1,-1,1,1,-1,-1,1,1,-1,- 1},{1,-1,1,1,-1,-1,1,1,-1,1},{1,- 1,1,1,-1,-1,1,1,1,-1},{1,-1,1,1,-1,- 1,1,1,1,1},{1,-1,1,1,-1,1,-1,-1,-1,- 1},{1,-1,1,1,-1,1,-1,-1,-1,1},{1,- 1,1,1,-1,1,-1,-1,1,-1},{1,-1,1,1,-1,1,- 1,-1,1,1},{1,-1,1,1,-1,1,-1,1,-1,- 1},{1,-1,1,1,-1,1,-1,1,-1,1},{1,- 1,1,1,-1,1,-1,1,1,-1},{1,-1,1,1,-1,1,- 1,1,1,1},{1,-1,1,1,-1,1,1,-1,-1,- 1},{1,-1,1,1,-1,1,1,-1,-1,1},{1,- 1,1,1,-1,1,1,-1,1,-1},{1,-1,1,1,- 1,1,1,-1,1,1},{1,-1,1,1,-1,1,1,1,-1,- 1},{1,-1,1,1,-1,1,1,1,-1,1},{1,-1,1,1,- 1,1,1,1,1,-1},{1,-1,1,1,- 1,1,1,1,1,1},{1,-1,1,1,1,-1,-1,-1,-1,- 1},{1,-1,1,1,1,-1,-1,-1,-1,1},{1,- Schrausser, D. G. (2025). HP_Prime_MATH: Manual. 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