laffernandes / gatl

GATL: Geometric Algebra Template Library
GNU General Public License v3.0
56 stars 5 forks source link

Revisar aplicação de simplificações na avaliação tardia #19

Closed laffernandes closed 5 years ago

laffernandes commented 6 years ago

0 + X = X X + 0 = X 0 + 0 = 0 A + 1/C = simpler (except for A == 0) 1/C + A = simpler (except for A == 0) A/B + 1/C = simpler (except for B == C) 1/C + A/B = simpler (except for C == B) 1/B + 1/C = simpler (except for B == C) A + A = 2 A A + (A + ...) = 2 A + ... ... + (P ...) = (1 + P) ... (P ...) + ... = (P + 1) ... (P ...) + (Q ...) = (P + Q) * ... A + (B + C) = (A + B) + C

A + (-B) = A - B = R

(-A) + B = B - A = R

(A C) + (B C) = (A + B) C (A C) + ((B C) + D) = (A + B) C + D ((A C) + D) + (B C) = (A + B) C + D (-1) A = -A A (-1) = -A A (1 / B) = A / B (1 / A) B = B / A (1 / A) (1 / B) = 1 / (A * B) pow(A, -1) = 1 / A pow(A, 1 / 2) = sqrt(A) pow(A, 1 / 3) = cbrt(A)

0^{X} = 0, for X > 0

1^{X} = 1

(-1)^{K} = 1, if K is odd = -1, if K is even

X^{0} = 1 X^{1} = X sqrt(X) = Y, if it is possible simplify for given integer X and Y values X^{Y} = simpler (A^{B})^{C} = A^{B C} (A B)^{C} = A^{C} * B^{C}