Expression of type Lambda

from the theory of proveit.physics.quantum.algebra

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, M, m, n
from proveit.linear_algebra import LinMap, MatrixSpace
from proveit.logic import CartExp, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
expr = Lambda(M, Conditional(InSet(Qmult(M), LinMap(CartExp(Complex, n), CartExp(Complex, m))), InSet(M, MatrixSpace(field = Complex, rows = m, columns = n))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

M \mapsto \left\{\left[M\right] \in \mathcal{L}\left(\mathbb{C}^{n}, \mathbb{C}^{m}\right) \textrm{ if } M \in \mathbb{C}^{m \times n}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 16 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	16, 9
7	Operation	operator: 10 operand: 16
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operands: 15
10	Literal
11	ExprTuple	16
12	Literal
13	ExprTuple	17, 18
14	Literal
15	NamedExprs	field: 23 rows: 24 columns: 22
16	Variable
17	Operation	operator: 20 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	23, 22
20	Literal
21	ExprTuple	23, 24
22	Variable
23	Literal
24	Variable