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(frac(one, Exp(two, frac(_t, 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(\frac{1}{2^{\frac{t}{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: 37 operands: 3
2	Operation	operator: 4 operand: 7
3	ExprTuple	43, 6
4	Literal
5	ExprTuple	7
6	Operation	operator: 46 operands: 8
7	Lambda	parameter: 50 body: 10
8	ExprTuple	52, 11
9	ExprTuple	50
10	Conditional	value: 12 condition: 13
11	Operation	operator: 37 operands: 14
12	Operation	operator: 44 operands: 15
13	Operation	operator: 16 operands: 17
14	ExprTuple	53, 52
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	50, 20
18	Operation	operator: 46 operands: 21
19	Operation	operator: 46 operands: 22
20	Operation	operator: 23 operands: 24
21	ExprTuple	26, 25
22	ExprTuple	26, 27
23	Literal
24	ExprTuple	28, 29
25	Operation	operator: 44 operands: 30
26	Literal
27	Operation	operator: 39 operand: 35
28	Literal
29	Operation	operator: 32 operands: 33
30	ExprTuple	52, 48, 49, 34, 50
31	ExprTuple	35
32	Literal
33	ExprTuple	42, 36
34	Literal
35	Operation	operator: 37 operands: 38
36	Operation	operator: 39 operand: 43
37	Literal
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	43
41	Operation	operator: 44 operands: 45
42	Operation	operator: 46 operands: 47
43	Literal
44	Literal
45	ExprTuple	52, 48, 49, 50, 51
46	Literal
47	ExprTuple	52, 53
48	Literal
49	Literal
50	Variable
51	Variable
52	Literal
53	Literal