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, one, pi, two
from proveit.physics.quantum.QPE import _m_domain, _phase, _t, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(Exp(frac(one, Exp(two, frac(_t, two))), two), 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(\left(\frac{1}{2^{\frac{t}{2}}}\right)^{2}, \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()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 48 operands: 3
2	Operation	operator: 4 operand: 7
3	ExprTuple	6, 54
4	Literal
5	ExprTuple	7
6	Operation	operator: 39 operands: 8
7	Lambda	parameter: 52 body: 10
8	ExprTuple	45, 11
9	ExprTuple	52
10	Conditional	value: 12 condition: 13
11	Operation	operator: 48 operands: 14
12	Operation	operator: 46 operands: 15
13	Operation	operator: 16 operands: 17
14	ExprTuple	54, 18
15	ExprTuple	19, 20
16	Literal
17	ExprTuple	52, 21
18	Operation	operator: 39 operands: 22
19	Operation	operator: 48 operands: 23
20	Operation	operator: 48 operands: 24
21	Operation	operator: 25 operands: 26
22	ExprTuple	55, 54
23	ExprTuple	28, 27
24	ExprTuple	28, 29
25	Literal
26	ExprTuple	30, 31
27	Operation	operator: 46 operands: 32
28	Literal
29	Operation	operator: 41 operand: 37
30	Literal
31	Operation	operator: 34 operands: 35
32	ExprTuple	54, 50, 51, 36, 52
33	ExprTuple	37
34	Literal
35	ExprTuple	44, 38
36	Literal
37	Operation	operator: 39 operands: 40
38	Operation	operator: 41 operand: 45
39	Literal
40	ExprTuple	43, 44
41	Literal
42	ExprTuple	45
43	Operation	operator: 46 operands: 47
44	Operation	operator: 48 operands: 49
45	Literal
46	Literal
47	ExprTuple	54, 50, 51, 52, 53
48	Literal
49	ExprTuple	54, 55
50	Literal
51	Literal
52	Variable
53	Variable
54	Literal
55	Literal