Expression of type Lambda

from the theory of proveit.physics.quantum.circuits

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 IndexedVar, Lambda, U, Variable
from proveit.linear_algebra import MatrixMult, ScalarMult
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, e, i, pi, two
from proveit.physics.quantum import var_ket_u, varphi

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(sub_expr1, Equals(MatrixMult(IndexedVar(U, sub_expr1), var_ket_u), ScalarMult(Exp(e, Mult(two, pi, i, IndexedVar(varphi, sub_expr1))), var_ket_u)))

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())

{_{-}a} \mapsto \left(\left(U_{{_{-}a}} \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{{_{-}a}}} \cdot \lvert u \rangle\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 26 body: 1
1	Operation	operator: 2 operands: 3
2	Literal
3	ExprTuple	4, 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 12
8	Literal
9	ExprTuple	11, 12
10	IndexedVar	variable: 13 index: 26
11	Operation	operator: 14 operands: 15
12	Variable
13	Variable
14	Literal
15	ExprTuple	16, 17
16	Literal
17	Operation	operator: 18 operands: 19
18	Literal
19	ExprTuple	20, 21, 22, 23
20	Literal
21	Literal
22	Literal
23	IndexedVar	variable: 24 index: 26
24	Variable
25	ExprTuple	26
26	Variable