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4 years ago asked a question Assume expression to be noninteger

Hello! How to assume expression to be an integer? I try to do some symbolic integration while Sage asks to provide additional info about expression. MWE:

var('x a b')
assume(b > 0)
f = (exp((x-a)/b) + 1)**(-1)
(f*f).integrate(x, 0, oo)

gives:

ValueError: Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation may help (example of legal syntax is 'assume((2a)/b>0)', see assume? for more details) Is (2a)/b an integer?

How to assume that (2*a)/b is an arbitrary positive real number? Straightforward assume((2*a)/b, 'noninteger') gives:

TypeError: self (=2*a/b) must be a relational expression

Thanks!

7 years ago commented answer Substitution of subexpression

Interesting and confusing.. Why do I have to include w in subexpression?

7 years ago asked a question Substitution of subexpression

Hi! My task is to derive some expression and then find subexpressions in it and substitute. In details I need to find derivative of psi and then substitute expressions back. The way I found this derivative looks ugly but I suppose it's easier to do substitution in such form of expression.

var('x, y, t, a, w, alpha, beta')
assume(w > 0)
assume(a > 0)
assume(x, y, t, 'real')
x1 = x*cos(w*t) + y*sin(w*t)
y1 = y*cos(w*t) - x*sin(w*t)

psi10 = 2/a * sin(2*pi/a*x2) * sin(pi/a*y2)
psi01 = 2/a * sin(pi/a*x2) * sin(2*pi/a*y2)

psi = alpha*psi10 + beta*psi01

psi_der = psi.diff(x2)*x1.diff(t) + psi.diff(y2)*y1.diff(t)
psi_der

2(wxcos(tw)+wysin(tw))(παcos(πy2a)sin(2πx2a)a2+2πβcos(2πy2a)sin(πx2a)a2)+ +2(wycos(tw)wxsin(tw))(πβcos(πx2a)sin(2πy2a)a2+2παcos(2πx2a)sin(πy2a)a2)

Then I need to substitute xcos(wt) + ysin(wt) to x2 and ycos(wt) - xsin(wt) to y2 for further integration over x2 and y2. Unfortunately, I didn't understand how to do this except that I need to use wild cards. So

w0 = SR.wild(0)
w1 = SR.wild(1)
pattern = x1*w0 + w1*y1
pattern

$0(xcos(tw)+ysin(tw))+$1(ycos(tw)xsin(tw)) which is looks pretty the same but somehow don't match:

print psi_der.match(pattern)

gives None.

Could someone explain what is going on or maybe I should use something else?