In the following example I would like to make Sage realize that (p,q,r)
are constants and (a,b) are variables
so in the end everything should be expressed as a polynomial in a,b. In
particular b^2 should be rewritten as 1-a^2
(b and a are actually sin and cosine of something) but b should not be
rewritten as sqrt(1-a^2). And,
in the end the terms should be grouped so we see explicitly the
coefficients of a,b,1, and a^2. Of course this
example is simple enough to do by hand, but I want to know how to control
Sage enough to get this to happen in Sage.
I tried various simplification functions. I suppose I could start over,
not using "symbolic expressions" but
declaring K to be a suitable field or ring, maybe a quadratic extension of
the field of rational functions in a.
That is probably the "right" way to do it. But I wish there were a
simpler way. I'm writing a paper with
little snippets of Sage code with which the reader, who will be a
mathematician probably unfamiliar with SageMath,
can check the computations, or see how the computations can be checked.
So the code should be readable to such a person, ruling out the
introduction
of new fields. The code below is perfectly readable in that sense, but
it doesn't quite do the job.
def mar11b():
var('p,q,r,a,b')
b = sqrt(1-a^2)
lam = p*a + r*b + q
mu = r*a - p*b
lam = sqrt(N/2)
eq = lam^2 - (p*a+r*b+q)^2
eq = eq.expand()
print(eq)
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