substitute

substitute(f,v) -- substitute values for the variables in the matrix, module, vector, polynomial, or monomial f as specified by v.

If f is a matrix over R, and v is a 1 by k matrix over another ring S, then the result is obtained by substituting the entries in v for the variables in R.

If f is a module over R, then substitution amounts to substitution in the matrices of generators and relations defining the module. This is not the same as tensor product!

If v is a ring, then the result is obtained by substituting the variables of v for the variables of R with the same name. The substitution extends to the coefficient ring of R, and so on.

If v is a list of options {a => f, b => g, ...} then the variable a is replaced by the polynomial f, etc.

i1 : R = ZZ/101[x,y,z]



o1 = R



o1 : PolynomialRing

i2 : f = x+2*y+3*z



o2 = x + 2y + 3z



o2 : R

i3 : substitute(f,{x=>x^3, y=>y^3})



      3     3

o3 = x  + 2y  + 3z



o3 : R

i4 : S = ZZ/101[z,y,x]



o4 = S



o4 : PolynomialRing

i5 : substitute(f,S)



o5 = 3z + 2y + x



o5 : S