How to define variables over integer

[Santanu Sarkar]

I know how to define variables over BooleanPolynomialRing.

This is as follows.

n=4

V=BooleanPolynomialRing(n+1,['z%d'%(i) for i in range(n+1)] )
V.inject_variables()

Can we define similar code over integers (ZZ) or rationals (QQ)?

Also I want to store variables in an array like Z=[z0,z1,z2,z3]

but it should be automatic. I will change only n.  

[darwin doppelganger]

Doesn't PolynomialRing() do what you want? For example,

n=4
V=PolynomialRing(QQ,n+1,['z%d'%(i) for i in range(n+1)] )
V.inject_variables()

[darwin doppelganger]

I forgot to add that you can automatically put the variables in a list with:

Z = list(V.gens())

[Simon King]

Hi Santanu,

Am Mittwoch, 8. Mai 2019 15:15:06 UTC+2 schrieb Santanu:

I know how to define variables over BooleanPolynomialRing.

This is as follows.

n=4

V=BooleanPolynomialRing(n+1,['z%d'%(i) for i in range(n+1)] )
V.inject_variables()

The above is what you could do in an interactive session in the case that the number of variables isn't known in advance. If it is known that you have exactly four variables, simply do

   sage: V.<z0,z1,z2,z3> = BooleanPolynomialRing()

which would automatically define z0,...,z3 in the global namespace.

Similarly, you can do

   sage: V.<z0,z1,z2,z3> = ZZ[]

to create a polynomial ring over the integers with generators z0,...,z3

But the above is not what you could do in a python module and in a module it is also a bad idea to inject variables.

So, simply put the variables in a list or access them by methods of V.

Can we define similar code over integers (ZZ) or rationals (QQ)?

Actually I wonder if we mean the same when we say "variables over ZZ". I mean "generators of a polynomial ring with integer coefficients". When the number of generators isn't known in advance, but the generators are named z0,z1,z2,..., such ring can be created, e.g., by

    sage: P = PolynomialRing(ZZ, 'z', 5)

    sage: P

    Multivariate Polynomial Ring in z0, z1, z2, z3, z4 over Integer Ring

However, I could imagine that you wanted to ask how to create a symbolic variable that is assumed to take values in ZZ --- and that's totally different from a generator of a polynomial ring over ZZ. So, if that's what you mean, you could do (in an interactive session)

    sage: var('z0 z1 z2 z3', domain='integer')

(which would inject the variables into the global namespace) or

    Z = var('z0 z1 z2 z3', domain='integer')

(which would also work in a python module and puts the variables into a tuple).

Also I want to store variables in an array like Z=[z0,z1,z2,z3]

but it should be automatic. I will change only n.

If you really want to work with symbolic variables, you could do

    sage: n = 5
    sage: Z = var(['z{}'.format(i) for i in range(n)], domain='integer')
    sage: Z
    (z0, z1, z2, z3, z4)
    sage: z0
    z0
(thus, the variables are both put in a tuple and injected into the global name space.

However, I believe that very many Sage users work with symbolic variables when they should better use generators of polynomial rings. So, perhaps code such as the following

    sage: P = PolynomialRing(ZZ, 'z', n)

    sage: Z = P.gens()

    sage: Z
    (z0, z1, z2, z3, z4)
    sage: P.gen(0)
    z0

    sage: P.inject_variables()

    Defining z0, z1, z2, z3, z4

(the latter only in an interactive session) suites your needs better.

Best regards,

Simon

[Santanu Sarkar]

Dear friends,

   Thank you so much for your help. It is working now.

Regards,

Santanu

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[Justin C. Walker]

Check out PolynomialRing. Typing
PolynomialRing?
will give you some documentation.

HTH

Justin

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