5fe3d7f4-41f6-49f6-84f1-199792e3a6b9 27 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Pascal Triangle ... automated companion

n 012345678910111 mat transpose :

x 1 :

CWD C:\SmathFile CurrentDirectory :

x Pa a x + (n^expand maple vectorize 11 line :

Add/Remove 'n' pairwise

x Pa CWD Pascal wfile 1

x p CWD Pascal rfile :

x Clear 1

a x :

x p 1 x 1 + x 2^2 x * + 1 + x 3^3 x 2^* + 3 x * + 1 + x 4^4 x 3^* + 6 x 2^* + 4 x * + 1 + x 5^5 x 4^* + 10 x 3^* + 10 x 2^* + 5 x * + 1 + x 6^6 x 5^* + 15 x 4^* + 20 x 3^* + 15 x 2^* + 6 x * + 1 + x 7^7 x 6^* + 21 x 5^* + 35 x 4^* + 35 x 3^* + 21 x 2^* + 7 x * + 1 + x 8^8 x 7^* + 28 x 6^* + 56 x 5^* + 70 x 4^* + 56 x 3^* + 28 x 2^* + 8 x * + 1 + x 9^9 x 8^* + 36 x 7^* + 84 x 6^* + 126 x 5^* + 126 x 4^* + 84 x 3^* + 36 x 2^* + 9 x * + 1 + x 10^10 x 9^* + 45 x 8^* + 120 x 7^* + 210 x 6^* + 252 x 5^* + 210 x 4^* + 120 x 3^* + 45 x 2^* + 10 x * + 1 + 111 mat

maple op( ■ ) dissociates the ± arithmetics elementwise x OP x p op maple vectorize transpose 11 mat 11 line :

x OP CWD Pascal_op wfile 1

x expr CWD Pascal_op rfile :

x 1 :

expr x expr :

index 1 to explode the transit expr expr 1 el :

vec Stack V 1 el vec 1 el : i 2 vec cols range u i 1 - el vec i el : for V u stack 31 line :

Triangle expr Stack :

Triangle 11112 mat 12113 mat 133114 mat 1464115 mat 1510105116 mat 161520156117 mat 17213535217118 mat 1828567056288119 mat 193684126126843691110 mat 1104512021025221012045101111 mat 111 mat

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

index 1 to explode the transit Ω Triangle Triangle rows row 1 el :

Ω 1104512021025221012045101111 mat

j 1 Ω cols range :

data j Ω transpose augment :

Pascal data . 12 black plot :

Pascal data 2 1 sys

data 11210345412052106252721081209451010111112 mat

User fabricate demo. scale 1011 : mean 6 : std 1.6 : 13 mat

Under the hood, Pascal represents the Normal PDF .

Pascal scale x mean std pdf.Normal * 2 1 sys

scale 6 mean std pdf.Normal * 252.1

jmG: 20230621