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, _psi_t_ket

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(_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()))

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(\lvert \psi_{t} \rangle, \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	1, 2
1	Operation	operator: 3 operand: 20
2	Operation	operator: 4 operands: 5
3	Literal
4	Literal
5	ExprTuple	6
6	ExprRange	lambda_map: 7 start_index: 8 end_index: 29
7	Lambda	parameter: 52 body: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 26 operands: 12
10	Literal
11	ExprTuple	13, 39
12	ExprTuple	14, 15
13	Operation	operator: 50 operand: 20
14	Operation	operator: 32 operands: 17
15	Operation	operator: 18 operands: 19
16	ExprTuple	20
17	ExprTuple	39, 21
18	Literal
19	ExprTuple	22, 23
20	Variable
21	Operation	operator: 46 operands: 24
22	Operation	operator: 35 operand: 29
23	Operation	operator: 26 operands: 27
24	ExprTuple	48, 28
25	ExprTuple	29
26	Literal
27	ExprTuple	30, 31
28	Operation	operator: 32 operands: 33
29	Literal
30	Operation	operator: 46 operands: 34
31	Operation	operator: 35 operand: 39
32	Literal
33	ExprTuple	39, 48
34	ExprTuple	37, 38
35	Literal
36	ExprTuple	39
37	Literal
38	Operation	operator: 40 operands: 41
39	Literal
40	Literal
41	ExprTuple	48, 42, 43, 44, 45
42	Literal
43	Literal
44	Operation	operator: 46 operands: 47
45	Literal
46	Literal
47	ExprTuple	48, 49
48	Literal
49	Operation	operator: 50 operand: 52
50	Literal
51	ExprTuple	52
52	Variable