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, TensorProd, 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(sub_expr2, TensorProd(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}}, \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right){\otimes} \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) {\otimes}  \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) {\otimes}  \ldots {\otimes}  \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	17, 1
1	Operation	operator: 2 operands: 3
2	Literal
3	ExprTuple	4, 5
4	Operation	operator: 22 operands: 6
5	ExprRange	lambda_map: 7 start_index: 8 end_index: 35
6	ExprTuple	26, 9
7	Lambda	parameter: 60 body: 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 31 operands: 13
10	Operation	operator: 31 operands: 14
11	Literal
12	ExprTuple	15, 47
13	ExprTuple	16, 37
14	ExprTuple	17, 18
15	Operation	operator: 58 operand: 44
16	Operation	operator: 54 operands: 20
17	Operation	operator: 39 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprTuple	44
20	ExprTuple	45, 24
21	ExprTuple	47, 25
22	Literal
23	ExprTuple	26, 27
24	Operation	operator: 48 operands: 28
25	Operation	operator: 54 operands: 29
26	Operation	operator: 42 operand: 35
27	Operation	operator: 31 operands: 32
28	ExprTuple	56, 50, 51, 33, 53
29	ExprTuple	56, 34
30	ExprTuple	35
31	Literal
32	ExprTuple	36, 37
33	Operation	operator: 54 operands: 38
34	Operation	operator: 39 operands: 40
35	Literal
36	Operation	operator: 54 operands: 41
37	Operation	operator: 42 operand: 47
38	ExprTuple	56, 44
39	Literal
40	ExprTuple	47, 56
41	ExprTuple	45, 46
42	Literal
43	ExprTuple	47
44	Variable
45	Literal
46	Operation	operator: 48 operands: 49
47	Literal
48	Literal
49	ExprTuple	56, 50, 51, 52, 53
50	Literal
51	Literal
52	Operation	operator: 54 operands: 55
53	Literal
54	Literal
55	ExprTuple	56, 57
56	Literal
57	Operation	operator: 58 operand: 60
58	Literal
59	ExprTuple	60
60	Variable