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, x
from proveit.linear_algebra import MatrixMult, MatrixSpace
from proveit.logic import CartExp, Equals, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
expr = Lambda(M, Conditional(Equals(Qmult(M), Lambda(x, Conditional(MatrixMult(M, x), InSet(x, CartExp(Complex, n))))), 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] = \left[x \mapsto \left\{M \thinspace x \textrm{ if } x \in \mathbb{C}^{n}\right..\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: 23 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 21 operands: 6
4	Literal
5	ExprTuple	7, 8
6	ExprTuple	23, 9
7	Operation	operator: 10 operand: 23
8	Lambda	parameter: 24 body: 13
9	Operation	operator: 14 operands: 15
10	Literal
11	ExprTuple	23
12	ExprTuple	24
13	Conditional	value: 16 condition: 17
14	Literal
15	NamedExprs	field: 28 rows: 18 columns: 29
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Variable
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	24, 25
23	Variable
24	Variable
25	Operation	operator: 26 operands: 27
26	Literal
27	ExprTuple	28, 29
28	Literal
29	Variable