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
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.numbers import Exp, Mult, e, frac, i, one, pi, two
from proveit.physics.quantum import NumKet
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))), 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}}}, {\mathrm {FT}}^{\dag}_{t}, \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)

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