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.linear_algebra import ScalarMult, VecSum
from proveit.numbers import Exp, Mult, e, frac, i, one, pi, two
from proveit.physics.quantum import NumBra, NumKet, Qmult
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _m_domain, _phase, _t

# build up the expression from sub-expressions
expr = ExprTuple(frac(one, Exp(two, frac(_t, two))), Qmult(NumBra(m, _t), InverseFourierTransform(_t), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, _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}}}, {_{t}}\langle m \rvert \thinspace {\mathrm {FT}}^{\dag}_{t} \thinspace \left(\sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{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: 20 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	58, 6
4	Literal
5	ExprTuple	7, 8, 9
6	Operation	operator: 52 operands: 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 13 operand: 57
9	Operation	operator: 15 operand: 19
10	ExprTuple	56, 17
11	Literal
12	ExprTuple	18, 57
13	Literal
14	ExprTuple	57
15	Literal
16	ExprTuple	19
17	Operation	operator: 20 operands: 21
18	Variable
19	Lambda	parameter: 49 body: 23
20	Literal
21	ExprTuple	57, 56
22	ExprTuple	49
23	Conditional	value: 24 condition: 25
24	Operation	operator: 26 operands: 27
25	Operation	operator: 28 operands: 29
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	49, 32
30	Operation	operator: 52 operands: 33
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operands: 37
33	ExprTuple	38, 39
34	Literal
35	ExprTuple	49, 57
36	Literal
37	ExprTuple	40, 41
38	Literal
39	Operation	operator: 42 operands: 43
40	Literal
41	Operation	operator: 44 operands: 45
42	Literal
43	ExprTuple	56, 46, 47, 48, 49
44	Literal
45	ExprTuple	50, 51
46	Literal
47	Literal
48	Literal
49	Variable
50	Operation	operator: 52 operands: 53
51	Operation	operator: 54 operand: 58
52	Literal
53	ExprTuple	56, 57
54	Literal
55	ExprTuple	58
56	Literal
57	Literal
58	Literal