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_mod_two_pow_t, _m_domain, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(_alpha_m_mod_two_pow_t, Mult(frac(one, _two_pow_t), Sum(index_or_indices = [k], summand = Mult(Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t))), Exp(e, Mult(two, pi, i, _phase, k))), 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 ~\textup{mod}~ 2^{t}}, \frac{1}{2^{t}} \cdot \left(\sum_{k = 0}^{2^{t} - 1} \left(\mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k}\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: 6
2	Operation	operator: 48 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 41 operands: 11
8	Operation	operator: 12 operand: 14
9	Literal
10	ExprTuple	55, 46
11	ExprTuple	47, 46
12	Literal
13	ExprTuple	14
14	Lambda	parameter: 54 body: 16
15	ExprTuple	54
16	Conditional	value: 17 condition: 18
17	Operation	operator: 48 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	54, 24
22	Operation	operator: 50 operands: 25
23	Operation	operator: 50 operands: 26
24	Operation	operator: 27 operands: 28
25	ExprTuple	30, 29
26	ExprTuple	30, 31
27	Literal
28	ExprTuple	32, 33
29	Operation	operator: 43 operand: 38
30	Literal
31	Operation	operator: 48 operands: 35
32	Literal
33	Operation	operator: 36 operands: 37
34	ExprTuple	38
35	ExprTuple	56, 52, 53, 39, 54
36	Literal
37	ExprTuple	46, 40
38	Operation	operator: 41 operands: 42
39	Literal
40	Operation	operator: 43 operand: 47
41	Literal
42	ExprTuple	45, 46
43	Literal
44	ExprTuple	47
45	Operation	operator: 48 operands: 49
46	Operation	operator: 50 operands: 51
47	Literal
48	Literal
49	ExprTuple	56, 52, 53, 54, 55
50	Literal
51	ExprTuple	56, 57
52	Literal
53	Literal
54	Variable
55	Variable
56	Literal
57	Literal