Unusual behaviour of the built-in complex numbers

[sagetrac-ljpk]

SAGE has a built-in copy of the complex numbers, so it knows what I is. However, one gets slightly odd behaviour from this:

sage: (1+I)^2 - 2*I

(1+I)^2 - 2*I

and one has to use the .expand() command to get the correct answer 2*I. This is not the behaviour of a user-defined quadratic field, which automatically evaluates such things. I think that the computation should resolve to 0 without having to be expanded.

CC: @mwhansen @sagetrac-mvngu

Component: commutative algebra

Issue created by migration from https://trac.sagemath.org/ticket/1680

[williamstein]

comment:2

This behavior of the symbolic I is imposed by Maxima. I do not know if there is any way to change it to behave like you want. You might want to use the I of the number field QQ(sqrt(-1))...

sage: I = NumberField(x^2 + 1, 'I').gen()
sage: (1+I)^2 - 2*I
0

Some day (who knows when) probably the Sage "I" will be the number field I, but where the number field is equipped with a canonical embedding in the symbolic ring, and then your example above will work as you want. I don't know when this will happen. It might not be too hard to implement.

William

[robertwb]

comment:3

This is certainly on the TODO list... currently for a number field

sage: I = NumberField(x^2 + 1, 'I').gen()

it doesn't know whether to send I to -I or I in CC, and a mechanism for this needs to be implemented.

[robertwb]

comment:4

Number fields now have embedddings, and these are used by the Pynac Symbolics. When that goes in, this ticket should be closed.

[jhpalmieri]

comment:5

I think this can be closed now.

[jasongrout]

comment:6

Please note the request to close this.

[mwhansen]

comment:7

Yep, this has been fixed.