logo

Expression of type LessEq

from the theory of proveit.physics.quantum.QPE

In [1]:
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 l
from proveit.numbers import Exp, LessEq, Sum, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [l]
expr = LessEq(Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(_diff_l_scaled_delta_floor, two)), domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(l, two)), domain = _neg_domain))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right) \leq \left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{l^{2}}\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 6
operand: 8
4Operationoperator: 6
operand: 9
5ExprTuple8
6Literal
7ExprTuple9
8Lambdaparameter: 34
body: 10
9Lambdaparameter: 34
body: 12
10Conditionalvalue: 13
condition: 15
11ExprTuple34
12Conditionalvalue: 14
condition: 15
13Operationoperator: 17
operands: 16
14Operationoperator: 17
operands: 18
15Operationoperator: 19
operands: 20
16ExprTuple62, 21
17Literal
18ExprTuple62, 22
19Literal
20ExprTuple34, 23
21Operationoperator: 50
operands: 24
22Operationoperator: 50
operands: 25
23Operationoperator: 26
operands: 27
24ExprTuple28, 56
25ExprTuple34, 56
26Literal
27ExprTuple29, 30
28Operationoperator: 54
operands: 31
29Operationoperator: 54
operands: 32
30Operationoperator: 60
operand: 37
31ExprTuple34, 35
32ExprTuple36, 62
33ExprTuple37
34Variable
35Operationoperator: 60
operand: 41
36Operationoperator: 60
operand: 42
37Operationoperator: 54
operands: 40
38ExprTuple41
39ExprTuple42
40ExprTuple43, 62
41Operationoperator: 44
operands: 45
42Operationoperator: 50
operands: 46
43Variable
44Literal
45ExprTuple47, 48
46ExprTuple56, 49
47Operationoperator: 50
operands: 51
48Operationoperator: 52
operand: 57
49Operationoperator: 54
operands: 55
50Literal
51ExprTuple56, 58
52Literal
53ExprTuple57
54Literal
55ExprTuple58, 59
56Literal
57Literal
58Literal
59Operationoperator: 60
operand: 62
60Literal
61ExprTuple62
62Literal