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 ExprRange, ExprTuple, Variable, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = frac(one, sqrt(two))
expr = ExprTuple(ScalarMult(sub_expr2, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, two_pow_t, _phase)), ket1))), ExprRange(sub_expr1, ScalarMult(sub_expr2, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1))), Add(Neg(t), one), zero).with_decreasing_order())

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