Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

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, ExprTuple, Lambda, k
from proveit.logic import Equals, InSet
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Exp(e, Mult(two, pi, i, _phase, k))
sub_expr2 = Exp(e, Mult(two, pi, i, _phase, two_pow_t))
expr = ExprTuple(Lambda(k, Conditional(Equals(Mult(sub_expr1, sub_expr2), Mult(sub_expr2, sub_expr1)), InSet(k, Interval(zero, subtract(two_pow_t, one))))))

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())

\left(k \mapsto \left\{\left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}}\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k}\right) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 38 body: 3
2	ExprTuple	38
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	38, 12
10	Operation	operator: 30 operands: 13
11	Operation	operator: 30 operands: 14
12	Operation	operator: 15 operands: 16
13	ExprTuple	18, 17
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 40 operands: 21
18	Operation	operator: 40 operands: 22
19	Literal
20	Operation	operator: 23 operands: 24
21	ExprTuple	26, 25
22	ExprTuple	26, 27
23	Literal
24	ExprTuple	34, 28
25	Operation	operator: 30 operands: 29
26	Literal
27	Operation	operator: 30 operands: 31
28	Operation	operator: 32 operand: 39
29	ExprTuple	42, 35, 36, 37, 34
30	Literal
31	ExprTuple	42, 35, 36, 37, 38
32	Literal
33	ExprTuple	39
34	Operation	operator: 40 operands: 41
35	Literal
36	Literal
37	Literal
38	Variable
39	Literal
40	Literal
41	ExprTuple	42, 43
42	Literal
43	Variable