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 Complex, 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), Complex)

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), \mathbb{C}\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: 5
2	Literal
3	Literal
4	ExprTuple	5
5	Lambda	parameter: 45 body: 7
6	ExprTuple	45
7	Conditional	value: 8 condition: 9
8	Operation	operator: 39 operands: 10
9	Operation	operator: 11 operands: 12
10	ExprTuple	13, 14
11	Literal
12	ExprTuple	45, 15
13	Operation	operator: 41 operands: 16
14	Operation	operator: 41 operands: 17
15	Operation	operator: 18 operands: 19
16	ExprTuple	21, 20
17	ExprTuple	21, 22
18	Literal
19	ExprTuple	23, 24
20	Operation	operator: 39 operands: 25
21	Literal
22	Operation	operator: 34 operand: 30
23	Literal
24	Operation	operator: 27 operands: 28
25	ExprTuple	47, 43, 44, 29, 45
26	ExprTuple	30
27	Literal
28	ExprTuple	37, 31
29	Literal
30	Operation	operator: 32 operands: 33
31	Operation	operator: 34 operand: 38
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38
36	Operation	operator: 39 operands: 40
37	Operation	operator: 41 operands: 42
38	Literal
39	Literal
40	ExprTuple	47, 43, 44, 45, 46
41	Literal
42	ExprTuple	47, 48
43	Literal
44	Literal
45	Variable
46	Variable
47	Literal
48	Literal