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 Conditional, ExprRange, ExprTuple, Lambda, Variable, t
from proveit.linear_algebra import ScalarMult, TensorProd, VecAdd
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Exp, Mult, NaturalPos, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase, _psi_t_ket

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

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(t \mapsto \left\{\lvert \psi_{t} \rangle = \left(\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) \textrm{ if } t \in \mathbb{N}^+\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 29 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	29, 11
9	Operation	operator: 12 operand: 29
10	Operation	operator: 13 operands: 14
11	Literal
12	Literal
13	Literal
14	ExprTuple	15
15	ExprRange	lambda_map: 16 start_index: 17 end_index: 38
16	Lambda	parameter: 61 body: 18
17	Operation	operator: 19 operands: 20
18	Operation	operator: 35 operands: 21
19	Literal
20	ExprTuple	22, 48
21	ExprTuple	23, 24
22	Operation	operator: 59 operand: 29
23	Operation	operator: 41 operands: 26
24	Operation	operator: 27 operands: 28
25	ExprTuple	29
26	ExprTuple	48, 30
27	Literal
28	ExprTuple	31, 32
29	Variable
30	Operation	operator: 55 operands: 33
31	Operation	operator: 44 operand: 38
32	Operation	operator: 35 operands: 36
33	ExprTuple	57, 37
34	ExprTuple	38
35	Literal
36	ExprTuple	39, 40
37	Operation	operator: 41 operands: 42
38	Literal
39	Operation	operator: 55 operands: 43
40	Operation	operator: 44 operand: 48
41	Literal
42	ExprTuple	48, 57
43	ExprTuple	46, 47
44	Literal
45	ExprTuple	48
46	Literal
47	Operation	operator: 49 operands: 50
48	Literal
49	Literal
50	ExprTuple	57, 51, 52, 53, 54
51	Literal
52	Literal
53	Operation	operator: 55 operands: 56
54	Literal
55	Literal
56	ExprTuple	57, 58
57	Literal
58	Operation	operator: 59 operand: 61
59	Literal
60	ExprTuple	61
61	Variable