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 ExprTuple, k, m
from proveit.numbers import Exp, Mult, Neg, Sum, e, frac, i, pi, two
from proveit.physics.quantum.QPE import _m_domain, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(Sum(index_or_indices = [k], summand = Mult(Exp(e, Mult(two, pi, i, _phase, k)), Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t)))), domain = _m_domain))

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(\sum_{k = 0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}}\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	Operation	operator: 2 operand: 4
2	Literal
3	ExprTuple	4
4	Lambda	parameter: 44 body: 6
5	ExprTuple	44
6	Conditional	value: 7 condition: 8
7	Operation	operator: 38 operands: 9
8	Operation	operator: 10 operands: 11
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	44, 14
12	Operation	operator: 40 operands: 15
13	Operation	operator: 40 operands: 16
14	Operation	operator: 17 operands: 18
15	ExprTuple	20, 19
16	ExprTuple	20, 21
17	Literal
18	ExprTuple	22, 23
19	Operation	operator: 38 operands: 24
20	Literal
21	Operation	operator: 33 operand: 29
22	Literal
23	Operation	operator: 26 operands: 27
24	ExprTuple	46, 42, 43, 28, 44
25	ExprTuple	29
26	Literal
27	ExprTuple	36, 30
28	Literal
29	Operation	operator: 31 operands: 32
30	Operation	operator: 33 operand: 37
31	Literal
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	37
35	Operation	operator: 38 operands: 39
36	Operation	operator: 40 operands: 41
37	Literal
38	Literal
39	ExprTuple	46, 42, 43, 44, 45
40	Literal
41	ExprTuple	46, 47
42	Literal
43	Literal
44	Variable
45	Variable
46	Literal
47	Literal