In SymPy, polynomials have extra structure that distinguishes them from
generic expressions. a3 * t**3 + a2 * t**2 + a1 * t + a0 is an expression.
If you create a polynomial in t, it will print with the order of terms
being from highest to lowest.
>>> p = sp.Poly([a3, a2, a1, a0], t)
>>> print(p)
Poly(a3*t**3 + a2*t**2 + a1*t + a0, t, domain='ZZ[a0,a1,a2,a3]')
Also, the order can be specified in the print command
>>> pprint(a3 * t**3 + a2 * t**2 + a1 * t + a0, order='grevlex')
3 2
a₃⋅t + a₂⋅t + a₁⋅t + a₀
or, staying with str format,
>>> sstrrepr(a3 * t**3 + a2 * t**2 + a1 * t + a0, order='grevlex')
'a3*t**3 + a2*t**2 + a1*t + a0'
The printing module <http://docs.sympy.org/latest/modules/printing.html> has
a number of printers which support a number of settings.
On Thursday, February 22, 2018 at 2:02:20 PM UTC-5, Matthias Geier wrote:
>
> Dear SymPy list.
>
> I'm playing around with polynomials in the context of spline curves.
>
> I want to use a cubic polynomial with yet unknown coefficients like this:
>
> >>> import sympy as sp
> >>> t, a0, a1, a2, a3 = sp.symbols('t, a:4', real=True)
> >>> a3 * t**3 + a2 * t**2 + a1 * t + a0
> a0 + a1*t + a2*t**2 + a3*t**3
>
> The problem here is that the displayed order of terms is reversed,
> normally the highest power of t should come first.
> I guess this is because SymPy doesn't know that the coefficients a0
> etc. are constants and shouldn't be treated like variables.
> So in fact this polynomial isn't sorted by powers of t but instead by
> the coefficients.
>
> Is there a way to get around this?
>
> At some later point, I have expressions like this (without t):
>
> a1 + 2*a2 + 3*a3
>
> It would make sense in my case to also display them reversed like this:
>
> 3*a3 + 2*a2 + a1
>
> Is it possible to create a new type of symbol with non-default ordering?
> Is it possible to define that this order is "ascending": a3, a2, a1, a0?
> It doesn't have to be a generic solution, I'm OK with having those 4
> special symbols.
>
> Or is there an entirely different and much better way to do this?
>
> I know that I could just use a, b, c, d instead of a3, a2, a1, a0 and
> it would work, but I would really like to see the connection between a
> coefficient and its power of t.
>
> For the record, I also quickly tried to use IndexedBase to get a3, a2,
> a1 and a0, and it turns out that although the LaTeX display of the
> symbols looks the same (in text mode it's different), they are sorted
> differently.
>
> >>> b = sp.IndexedBase('b')
> >>> b[3] * t**3 + b[2] * t**2 + b[1] * t + b[0]
> t**3*b[3] + t**2*b[2] + t*b[1] + b[0]
>
> They are sorted after the powers of t, which isn't what I want, either.
>
> cheers,
> Matthias
>
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