# How to create a coercion on hyperbolic models?

I want to put some text on my plots of the poincare disc model. I tried to do something like that,

word = text('my word',(real_part(P),imag_part(P)), color='black')


and gives me the following error,

TypeError: cannot coerce arguments: no canonical coercion from
Hyperbolic plane in the Poincare Disk Model to Symbolic Ring


Furthermore, this only works if my complex number P comes from the ring of complex numbers, not for a hyperbolic point. I need to configure some coercion. As substracting imaginary and real parts of a number in the poincare disk model. get_point method only work in one direction.

I am generating list of points like this.

Point in PD 0.150615998712507 - 0.101793686778004*I


and I want to add text in that coordinates, but I cannot find a way to coerce and get for example the complex number 0.1506 - 0.1017*I (even such exaggerate approximation will work in a plot)

Surely I am missing a method. Can you help me with this?

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First, you really need to provide the explicit construction of th objects, so that we can try to reproduce.

Without more information, let me assume that the P you speak about is of this form:

sage: H = HyperbolicPlane().PD()
sage: P = H.random_element()
sage: P
Point in PD 0.457058290632951 - 0.778395192442617*I


Indeed:

sage: real_part(P)
TypeError: cannot coerce arguments: no canonical coercion from Hyperbolic plane in the Poincare Disk Model to Symbolic Ring


To find a method related to some object, a very nice way is to use tab-completion, that is you type:

sage: P.<TAB>


Where <TAB> stands for the tab-key (which looks like two arrows on your keyboard).

There, you will find:

sage: P.coordinates()
0.457058290632951 - 0.778395192442617*I
sage: parent(P.coordinates())
Symbolic Ring


Which looks good, given the previous error message, and indeed, the following works:

sage: C = P.coordinates()
sage: word = text('my word',(real_part(C),imag_part(C)), color='black')
sage: word
Launched png viewer for Graphics object consisting of 1 graphics primitive

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What an amazing trick! I had no idea of the existence of the <tab> function!

( 2019-01-29 19:29:15 -0500 )edit

This is the first thing i teach during Sage trainings !

( 2019-01-30 03:52:34 -0500 )edit