Mapping a list to some variables for a system of equations

Anonymous

I have a list of integers $(a, b, c, d)$ and a system of equations, where each equation has two unknowns. My system looks like $(x0+x4, x1+x4, x2+x4, x3+x4).$ I am trying to evaluate the system in $(a,b,c,d)$ . If I write $system(x0=1, x1=2, x3=1, x4=1)$ , the system correctly outputs the result of each equation. Now, I would like to do something like $system(x0=a, x1=b, x3=c, x4=d)$ but without having to manually put the variables in. I have tried writing $system(list)$ but the number of variables and unknown doesn't match. Is there any way I can achieve this ?

answered 8 years ago

mforets
1413 ●9 ●27 ●44 http://marcelo-forets.fr/

updated 8 years ago

maybe using substitute:

sage: var('a, b, c, d')
(a, b, c, d)
sage: assume([(a, 'integer'), (b, 'integer'), (c, 'integer'), (d, 'integer')])
sage: x = polygens(ZZ, ['x'+str(i) for i in range(5)])    # create x_0, ..., x_4
sage: system = [x[0]+x[4], x[1]+x[4], x[2]+x[4], x[3]+x[4]]    # this is a Python list    
sage: evaluation = {x[0]:a, x[1]:b, x[3]:c, x[4]:d}    # this is a Python dictionary 
sage: [si.subs(evaluation) for si in system]   # subs is a shortcut for substitute
[a + d, b + d, d + x2, c + d]

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