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 _alpha_m, _m_domain, _phase, _t, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(_alpha_m, Mult(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(\alpha_{m}, \left(\frac{1}{2^{\frac{t}{2}}}\right)^{2} \cdot \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)\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: 3 operand: 58
2	Operation	operator: 51 operands: 5
3	Literal
4	ExprTuple	58
5	ExprTuple	6, 7
6	Operation	operator: 53 operands: 8
7	Operation	operator: 9 operand: 12
8	ExprTuple	11, 59
9	Literal
10	ExprTuple	12
11	Operation	operator: 44 operands: 13
12	Lambda	parameter: 57 body: 15
13	ExprTuple	50, 16
14	ExprTuple	57
15	Conditional	value: 17 condition: 18
16	Operation	operator: 53 operands: 19
17	Operation	operator: 51 operands: 20
18	Operation	operator: 21 operands: 22
19	ExprTuple	59, 23
20	ExprTuple	24, 25
21	Literal
22	ExprTuple	57, 26
23	Operation	operator: 44 operands: 27
24	Operation	operator: 53 operands: 28
25	Operation	operator: 53 operands: 29
26	Operation	operator: 30 operands: 31
27	ExprTuple	60, 59
28	ExprTuple	33, 32
29	ExprTuple	33, 34
30	Literal
31	ExprTuple	35, 36
32	Operation	operator: 51 operands: 37
33	Literal
34	Operation	operator: 46 operand: 42
35	Literal
36	Operation	operator: 39 operands: 40
37	ExprTuple	59, 55, 56, 41, 57
38	ExprTuple	42
39	Literal
40	ExprTuple	49, 43
41	Literal
42	Operation	operator: 44 operands: 45
43	Operation	operator: 46 operand: 50
44	Literal
45	ExprTuple	48, 49
46	Literal
47	ExprTuple	50
48	Operation	operator: 51 operands: 52
49	Operation	operator: 53 operands: 54
50	Literal
51	Literal
52	ExprTuple	59, 55, 56, 57, 58
53	Literal
54	ExprTuple	59, 60
55	Literal
56	Literal
57	Variable
58	Variable
59	Literal
60	Literal