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 _ket_u, _phase, _psi_t_ket

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

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(\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) {\otimes} \lvert u \rangle, \lvert \psi_{t} \rangle {\otimes} \lvert u \rangle\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: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 8
4	Literal
5	ExprTuple	7, 8
6	ExprRange	lambda_map: 9 start_index: 10 end_index: 32
7	Operation	operator: 11 operand: 23
8	Literal
9	Lambda	parameter: 55 body: 12
10	Operation	operator: 13 operands: 14
11	Literal
12	Operation	operator: 29 operands: 15
13	Literal
14	ExprTuple	16, 42
15	ExprTuple	17, 18
16	Operation	operator: 53 operand: 23
17	Operation	operator: 35 operands: 20
18	Operation	operator: 21 operands: 22
19	ExprTuple	23
20	ExprTuple	42, 24
21	Literal
22	ExprTuple	25, 26
23	Variable
24	Operation	operator: 49 operands: 27
25	Operation	operator: 38 operand: 32
26	Operation	operator: 29 operands: 30
27	ExprTuple	51, 31
28	ExprTuple	32
29	Literal
30	ExprTuple	33, 34
31	Operation	operator: 35 operands: 36
32	Literal
33	Operation	operator: 49 operands: 37
34	Operation	operator: 38 operand: 42
35	Literal
36	ExprTuple	42, 51
37	ExprTuple	40, 41
38	Literal
39	ExprTuple	42
40	Literal
41	Operation	operator: 43 operands: 44
42	Literal
43	Literal
44	ExprTuple	51, 45, 46, 47, 48
45	Literal
46	Literal
47	Operation	operator: 49 operands: 50
48	Literal
49	Literal
50	ExprTuple	51, 52
51	Literal
52	Operation	operator: 53 operand: 55
53	Literal
54	ExprTuple	55
55	Variable