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<H2><A ID="SECTION00013000000000000000">
Multi-Line Displays</A>
</H2>
<P>
<I>Scientific Notebook</I> provides a range of alignment options for
multiline mathematical displays. Here is a series of multiline displays.
<BR>
<DIV ALIGN="CENTER">
<!– MATH
x |
= |
17y 2 |
(1) |
y |
> |
a + b + c + d + e + f + g + h + i + j + |
|
|
|
k + l + m + n + o + p 3 |
(2) |
–>
<TABLE CELLPADDING="0" ALIGN="CENTER" WIDTH="100<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><I>x</I></TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP>=</TD>
<TD ALIGN="LEFT" NOWRAP>17<I>y</I><IMG
STYLE="" SRC="img8.png"
ALT="
">2</TD>
<TD WIDTH=10 ALIGN="RIGHT">
(1)</TD></TR>
<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><I>y</I></TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP>></TD>
<TD ALIGN="LEFT" NOWRAP><I>a</I> + <I>b</I> + <I>c</I> + <I>d</I> + <I>e</I> + <I>f</I> + <I>g</I> + <I>h</I> + <I>i</I> + <I>j</I> +</TD>
<TD WIDTH=10 ALIGN="RIGHT">
</TD></TR>
<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"> </TD>
<TD> </TD>
<TD ALIGN="LEFT" NOWRAP><I>k</I> + <I>l</I> + <I>m</I> + <I>n</I> + <I>o</I> + <I>p</I><IMG
STYLE="" SRC="img8.png"
ALT="
">3</TD>
<TD WIDTH=10 ALIGN="RIGHT">
(2)</TD></TR>
</TABLE></DIV>
<BR CLEAR="ALL">
<BR>
<DIV ALIGN="CENTER">
<!– MATH
x |
 |
y1 + ... + yn |
|
|
≤ |
z |
|
–>
<TABLE CELLPADDING="0" ALIGN="CENTER" WIDTH="100<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><I>x</I></TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP><IMG
STYLE="" SRC="img9.png"
ALT="
"></TD>
<TD ALIGN="LEFT" NOWRAP><I>y</I><SUB>1</SUB> + <SUP> ... </SUP> + <I>y</I><SUB>n</SUB></TD>
<TD WIDTH=10 ALIGN="RIGHT">
</TD></TR>
<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"> </TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP>≤</TD>
<TD ALIGN="LEFT" NOWRAP><I>z</I></TD>
<TD WIDTH=10 ALIGN="RIGHT">
</TD></TR>
</TABLE></DIV>
<BR CLEAR="ALL">
<BR>
<DIV ALIGN="CENTER">
<!– MATH
y |
= |
a + b + c + d + e + f + g + h + i + j |
|
|
|
+ k + l + m + n + o + p |
|
–>
<TABLE CELLPADDING="0" ALIGN="CENTER" WIDTH="100<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><I>y</I></TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP>=</TD>
<TD ALIGN="LEFT" NOWRAP><I>a</I> + <I>b</I> + <I>c</I> + <I>d</I> + <I>e</I> + <I>f</I> + <I>g</I> + <I>h</I> + <I>i</I> + <I>j</I></TD>
<TD WIDTH=10 ALIGN="RIGHT">
</TD></TR>
<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"> </TD>
<TD> </TD>
<TD ALIGN="LEFT" NOWRAP> + <I>k</I> + <I>l</I> + <I>m</I> + <I>n</I> + <I>o</I> + <I>p</I></TD>
<TD WIDTH=10 ALIGN="RIGHT">
</TD></TR>
</TABLE></DIV>
<BR CLEAR="ALL">
<BR>
<DIV ALIGN="CENTER">
<!– MATH
w + x + y + z |
= |
|
|
|
|
a + b + c + d + e + f + g + h + i + j + |
|
|
|
k + l + m + n + o + p |
|
–>
<TABLE CELLPADDING="0" ALIGN="CENTER" WIDTH="100<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><I>w</I> + <I>x</I> + <I>y</I> + <I>z</I></TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP>=</TD>
<TD> </TD>
<TD WIDTH=10 ALIGN="RIGHT">
</TD></TR>
<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"> </TD>
<TD> </TD>
<TD ALIGN="LEFT" NOWRAP><I>a</I> + <I>b</I> + <I>c</I> + <I>d</I> + <I>e</I> + <I>f</I> + <I>g</I> + <I>h</I> + <I>i</I> + <I>j</I> +</TD>
<TD WIDTH=10 ALIGN="RIGHT">
</TD></TR>
<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"> </TD>
<TD> </TD>
<TD ALIGN="LEFT" NOWRAP><I>k</I> + <I>l</I> + <I>m</I> + <I>n</I> + <I>o</I> + <I>p</I></TD>
<TD WIDTH=10 ALIGN="RIGHT">
</TD></TR>
</TABLE></DIV>
<BR CLEAR="ALL">
<P>
If <I>f</I> (<I>x</I>) = <I>x</I> + 1, then we will have
<P><!– MATH
f ([x + 1]/[x + 2]) = {[x + 1]/[x + 2]} + 1 = (2x + 3)/(x + 2)
–>
</P>
<DIV ALIGN="CENTER">
<I>f</I> ([<I>x</I> + 1]/[<I>x</I> + 2]) = [<I>x</I> + 1]/[<I>x</I> + 2] + 1 = (2<I>x</I> + 3)/(<I>x</I> + 2)
</DIV><P></P>
<BR>
<DIV ALIGN="CENTER">
<!– MATH
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 |
|
|
|
+13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 |
= |
190 |
|
–>
<TABLE CELLPADDING="0" ALIGN="CENTER" WIDTH="100<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT">1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12</TD>
<TD> </TD>
<TD> </TD>
<TD WIDTH=10 ALIGN="RIGHT">
</TD></TR>
<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT">+13 + 14 + 15 + 16 + 17 + 18 + 19 + 20</TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP>=</TD>
<TD ALIGN="LEFT" NOWRAP>190</TD>
<TD WIDTH=10 ALIGN="RIGHT">
</TD></TR>
</TABLE></DIV>
<BR CLEAR="ALL">
<P>
<BR>
<DIV ALIGN="CENTER">
<!– MATH
max(f, g) |
= |
, 4 |
(3) |
max(f, - g) |
= |
. 5 |
(4) |
–>
<TABLE CELLPADDING="0" ALIGN="CENTER" WIDTH="100<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT">max(<I>f</I>, <I>g</I>)</TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP>=</TD>
<TD ALIGN="LEFT" NOWRAP><IMG
STYLE="" SRC="img10.png"
ALT="
">,<IMG
STYLE="" SRC="img8.png"
ALT="
">4</TD>
<TD WIDTH=10 ALIGN="RIGHT">
(3)</TD></TR>
<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT">max(<I>f</I>, - <I>g</I>)</TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP>=</TD>
<TD ALIGN="LEFT" NOWRAP><IMG
STYLE="" SRC="img11.png"
ALT="
">.<IMG
STYLE="" SRC="img8.png"
ALT="
">5</TD>
<TD WIDTH=10 ALIGN="RIGHT">
(4)</TD></TR>
</TABLE></DIV>
<BR CLEAR="ALL">
<BR>
<DIV ALIGN="CENTER">
<!– MATH
(a + b)n+1 |
= |
(a + b)(a + b)n = (a + b) an-1bj 6 |
(5) |
|
= |
 an+1-jbj +  an-1bj 7 |
(6) |
|
= |
 an+1-jbj. 8 |
(7) |
–>
<TABLE CELLPADDING="0" ALIGN="CENTER" WIDTH="100<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT">(<I>a</I> + <I>b</I>)<SUP>n+1</SUP></TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP>=</TD>
<TD ALIGN="LEFT" NOWRAP>(<I>a</I> + <I>b</I>)(<I>a</I> + <I>b</I>)<SUP>n</SUP> = (<I>a</I> + <I>b</I>)<IMG
STYLE="" SRC="img12.png"
ALT="
"><IMG
STYLE="" SRC="img13.png"
ALT="
"><I>a</I><SUP>n-1</SUP><I>b</I><SUP>j</SUP><IMG
STYLE="" SRC="img8.png"
ALT="
">6</TD>
<TD WIDTH=10 ALIGN="RIGHT">
(5)</TD></TR>
<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"> </TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP>=</TD>
<TD ALIGN="LEFT" NOWRAP><IMG
STYLE="" SRC="img12.png"
ALT="
"><IMG
STYLE="" SRC="img13.png"
ALT="
"><I>a</I><SUP>n+1-j</SUP><I>b</I><SUP>j</SUP> + <IMG
STYLE="" SRC="img14.png"
ALT="
"><IMG
STYLE="" SRC="img15.png"
ALT="
"><I>a</I><SUP>n-1</SUP><I>b</I><SUP>j</SUP><IMG
STYLE="" SRC="img8.png"
ALT="
">7</TD>
<TD WIDTH=10 ALIGN="RIGHT">
(6)</TD></TR>
<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"> </TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP>=</TD>
<TD ALIGN="LEFT" NOWRAP><IMG
STYLE="" SRC="img12.png"
ALT="
"><IMG
STYLE="" SRC="img16.png"
ALT="
"><I>a</I><SUP>n+1-j</SUP><I>b</I><SUP>j</SUP>.<IMG
STYLE="" SRC="img8.png"
ALT="
">8</TD>
<TD WIDTH=10 ALIGN="RIGHT">
(7)</TD></TR>
</TABLE></DIV>
<BR CLEAR="ALL">
<P>
Test the overriding of automatic equation labels:
<BR>
<DIV ALIGN="CENTER">
<!– MATH
x |
= |
y + z A–1 |
(8) |
|
= |
k + m A–2 |
(9) |
–>
<TABLE CELLPADDING="0" ALIGN="CENTER" WIDTH="100<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><I>x</I></TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP>=</TD>
<TD ALIGN="LEFT" NOWRAP><I>y</I> + <I>z</I><IMG
STYLE="" SRC="img8.png"
ALT="
"><I>A</I>–1</TD>
<TD WIDTH=10 ALIGN="RIGHT">
(8)</TD></TR>
<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"> </TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP>=</TD>
<TD ALIGN="LEFT" NOWRAP><I>k</I> + <I>m</I><IMG
STYLE="" SRC="img8.png"
ALT="
"><I>A</I>–2</TD>
<TD WIDTH=10 ALIGN="RIGHT">
(9)</TD></TR>
</TABLE></DIV>
<BR CLEAR="ALL">
Test the overriding of automatic equation labels, suppressing annotation:
<BR>
<DIV ALIGN="CENTER">
<!– MATH
x |
= |
y + z *A–1 |
(10) |
|
= |
k + m *A–2 |
(11) |
–>
<TABLE CELLPADDING="0" ALIGN="CENTER" WIDTH="100<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><I>x</I></TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP>=</TD>
<TD ALIGN="LEFT" NOWRAP><I>y</I> + <I>z</I><IMG
STYLE="" SRC="img8.png"
ALT="
">*<I>A</I>–1</TD>
<TD WIDTH=10 ALIGN="RIGHT">
(10)</TD></TR>
<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"> </TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP>=</TD>
<TD ALIGN="LEFT" NOWRAP><I>k</I> + <I>m</I><IMG
STYLE="" SRC="img8.png"
ALT="
">*<I>A</I>–2</TD>
<TD WIDTH=10 ALIGN="RIGHT">
(11)</TD></TR>
</TABLE></DIV>
<BR CLEAR="ALL">
<P>
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