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, t
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = Exp(e, Mult(two, pi, i, _phase, k))
sub_expr3 = TensorProd(ket1, NumKet(k, t))
sub_expr4 = Exp(e, Mult(two, pi, i, _phase, two_pow_t))
sub_expr5 = Interval(zero, subtract(two_pow_t, one))
expr = ExprTuple(ScalarMult(sub_expr4, VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, sub_expr3), domain = sub_expr5)), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Mult(sub_expr4, sub_expr2), sub_expr3), domain = sub_expr5))

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(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \left(\sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{t}\right)\right)\right), \sum_{k=0}^{2^{t} - 1} \left(\left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k}\right) \cdot \left(\lvert 1 \rangle {\otimes} \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: 18 operands: 3
2	Operation	operator: 7 operand: 6
3	ExprTuple	25, 5
4	ExprTuple	6
5	Operation	operator: 7 operand: 10
6	Lambda	parameter: 53 body: 9
7	Literal
8	ExprTuple	10
9	Conditional	value: 11 condition: 16
10	Lambda	parameter: 53 body: 13
11	Operation	operator: 18 operands: 14
12	ExprTuple	53
13	Conditional	value: 15 condition: 16
14	ExprTuple	17, 23
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Operation	operator: 46 operands: 22
18	Literal
19	ExprTuple	26, 23
20	Literal
21	ExprTuple	53, 24
22	ExprTuple	25, 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 29 operands: 30
25	Operation	operator: 56 operands: 31
26	Operation	operator: 56 operands: 32
27	Literal
28	ExprTuple	33, 34
29	Literal
30	ExprTuple	35, 36
31	ExprTuple	38, 37
32	ExprTuple	38, 39
33	Operation	operator: 40 operand: 58
34	Operation	operator: 41 operands: 42
35	Literal
36	Operation	operator: 43 operands: 44
37	Operation	operator: 46 operands: 45
38	Literal
39	Operation	operator: 46 operands: 47
40	Literal
41	Literal
42	ExprTuple	53, 60
43	Literal
44	ExprTuple	49, 48
45	ExprTuple	59, 50, 51, 52, 49
46	Literal
47	ExprTuple	59, 50, 51, 52, 53
48	Operation	operator: 54 operand: 58
49	Operation	operator: 56 operands: 57
50	Literal
51	Literal
52	Literal
53	Variable
54	Literal
55	ExprTuple	58
56	Literal
57	ExprTuple	59, 60
58	Literal
59	Literal
60	Variable